Decimals

Given:

8.1, 9.4, 6.05, 12

To convert into like decimals, we make the number of decimal places equal.

The maximum number of decimal places is 2 (in 6.05).

So,

8.1 = 8.10
9.4 = 9.40
6.05 = 6.05
12 = 12.00

∴ Like decimals are 8.10, 9.40, 6.05 and 12.00

Given:

6.35, 11.8, 9.125, 32.04, 9

The maximum number of decimal places is 3 (in 9.125).

So,

6.35 = 6.350
11.8 = 11.800
9.125 = 9.125
32.04 = 32.040
9 = 9.000

∴ Like decimals are 6.350, 11.800, 9.125, 32.040 and 9.000

Given:

6.005, 2, 0.6, 1.78, 14.3

The maximum number of decimal places is 3 (in 6.005).

So,

6.005 = 6.005
2 = 2.000
0.6 = 0.600
1.78 = 1.780
14.3 = 14.300

∴ Like decimals are 6.005, 2.000, 0.600, 1.780 and 14.300

Given:

0.72, 53.76, 16, 8.304, 2.3754

Maximum decimal places = 4

So,

0.72 = 0.7200
53.76 = 53.7600
16 = 16.0000
8.304 = 8.3040
2.3754 = 2.3754

∴ Like decimals are 0.7200, 53.7600, 16.0000, 8.3040 and 2.3754

We have:

16.74 = 10 + 6 + 0.7 + 0.04 $\hspace{2cm}$[Separating according to place values]

$$\begin{aligned}= (1 \times 10) + (6 \times 1) + \Big(7 \times \frac{1}{10}\Big) + \Big(4 \times\frac{1}{100}\Big) \\[1em] = 10 + 6 + \frac{7}{10} + \frac{4}{100}\end{aligned}$$

∴ The expanded form of 16.74 is $\Big(10 + 6 + \frac{7}{10} + \frac{4}{100}\Big)$

We have:

243.689 = 200 + 40 + 3 + 0.6 + 0.08 + 0.009 [Separating according to place values]

$$\begin{aligned}= (2 \times 100) + (4 \times 10) + (3 \times 1) + \Big(6 \times \frac{1}{10}\Big) + \Big(8 \times \frac{1}{100}\Big) + \Big(9 \times \frac{1}{1000}\Big) \\[1em] = 200 + 40 + 3 + \frac{6}{10} + \frac{8}{100} + \frac{9}{1000}\end{aligned}$$

∴ The expanded form of 243.689 is $\Big(200 + 40 + 3 + \frac{6}{10} + \frac{8}{100} + \frac{9}{1000}\Big)$

We have:

9.3578 = 9 + 0.3 + 0.05 + 0.007 + 0.0008 [Separating according to place values]

$$\begin{aligned}= (9 \times 1) + \Big(3 \times \frac{1}{10}\Big) + \Big(5 \times \frac{1}{100}\Big) + \Big(7 \times \frac{1}{1000}\Big) + \Big(8 \times \frac{1}{10000}\Big) \\[1em] = 9 + \frac{3}{10} + \frac{5}{100} + \frac{7}{1000} + \frac{8}{10000}\end{aligned}$$

∴ The expanded form of 9.3578 is $\Big(9 + \frac{3}{10} + \frac{5}{100} + \frac{7}{1000} + \frac{8}{10000}\Big)$

We have:

2314.57 = 2000 + 300 + 10 + 4 + 0.5 + 0.07 [Separating according to place values]

$$\begin{aligned}= (2 \times 1000) + (3 \times 100) + (1 \times 10) + (4 \times 1) + \Big(5 \times \frac{1}{10}\Big) + \Big(7 \times \frac{1}{100}\Big) \\[1em] = 2000 + 300 + 10 + 4 + \frac{5}{10} + \frac{7}{100}\end{aligned}$$

∴ The expanded form of 2314.57 is $\Big(2000 + 300 + 10 + 4 + \frac{5}{10} + \frac{7}{100}\Big)$

We have:

0.8

There is 1 decimal place, so we remove the decimal point and divide by 10.

$$\begin{aligned}\phantom{=} 0.8 = \frac{8}{10} \\[1em] = \frac{4}{5} \quad \text{[Dividing both by 2]}\end{aligned}$$

∴ The answer is $\frac{4}{5}$

We have:

0.45

There are 2 decimal places, so we remove the decimal point and divide by 100.

$$\begin{aligned}\phantom{=} 0.45 = \frac{45}{100} \\[1em] = \frac{9}{20} \quad \text{[Dividing both by 5]}\end{aligned}$$

∴ The answer is $\frac{9}{20}$

We have:

1.6

There is 1 decimal place, so we remove the decimal point and divide by 10.

$$\begin{aligned}\phantom{=} 1.6 = \frac{16}{10} \\[1em] = \frac{8}{5} \quad \text{[Dividing both by 2]} \\[1em] = 1\frac{3}{5}\end{aligned}$$

∴ The answer is $1\frac{3}{5}$

We have:

4.75

There are 2 decimal places, so we remove the decimal point and divide by 100.

$$\begin{aligned}\phantom{=} 4.75 = \frac{475}{100} \\[1em] = \frac{19}{4} \quad \text{[Dividing both by 25]} \\[1em] = 4\frac{3}{4}\end{aligned}$$

∴ The answer is $4\frac{3}{4}$

We have:

0.345

There are 3 decimal places, so we remove the decimal point and divide by 1000.

$$\begin{aligned}\phantom{=} 0.345 = \frac{345}{1000} \\[1em] = \frac{69}{200} \quad \text{[Dividing both by 5]}\end{aligned}$$

∴ The answer is $\frac{69}{200}$

We have:

64.015

There are 3 decimal places, so we remove the decimal point and divide by 1000.

$$\begin{aligned}\phantom{=} 64.015 = \frac{64015}{1000} \\[1em] = \frac{12803}{200} \quad \text{[Dividing both by 5]} \\[1em] = 64\frac{3}{200}\end{aligned}$$

∴ The answer is $64\frac{3}{200}$

We have:

12.725

There are 3 decimal places, so we remove the decimal point and divide by 1000.

$$\begin{aligned}\phantom{=} 12.725 = \frac{12725}{1000} \\[1em] = \frac{509}{40} \quad \text{[Dividing both by 25]} \\[1em] = 12\frac{29}{40}\end{aligned}$$

∴ The answer is $12\frac{29}{40}$

We have:

0.0024

There are 4 decimal places, so we remove the decimal point and divide by 10000.

$$\begin{aligned}\phantom{=} 0.0024 = \frac{24}{10000} \\[1em] = \frac{3}{1250} \quad \text{[Dividing both by 8]}\end{aligned}$$

∴ The answer is $\frac{3}{1250}$

We have:

$$\begin{aligned}\phantom{=} \frac{19}{10} = 1\frac{9}{10} \quad \text{[improper to mixed]} \\[1em] = 1 + \frac{9}{10} \\[1em] = 1 + 0.9 \\[1em] = 1.9\end{aligned}$$

∴ The answer is 1.9

We have:

$$\begin{aligned}\phantom{=} \frac{243}{100} = 2\frac{43}{100} \quad \text{[improper to mixed]} \\[1em] = 2 + \frac{43}{100} \\[1em] = 2 + 0.43 \\[1em] = 2.43\end{aligned}$$

∴ The answer is 2.43

We have:

$\frac{51}{100} = 0.51$

∴ The answer is 0.51

We have:

$\frac{9}{100} = 0.09$

∴ The answer is 0.09

We have:

$\frac{72}{1000} = 0.072$

∴ The answer is 0.072

We have:

$$\begin{aligned}\phantom{=} \frac{3}{5} = \frac{3 \times 2}{5 \times 2} \quad \text{[Multiplying by 2 to get denominator 10]} \\[1em] = \frac{6}{10} \\[1em] = 0.6\end{aligned}$$

∴ The answer is 0.6

We have:

$$\begin{aligned}\phantom{=} \frac{7}{8} = \frac{7 \times 125}{8 \times 125} \quad \text{[Multiplying by 125 to get denominator 1000]} \\[1em] = \frac{875}{1000} \\[1em] = 0.875\end{aligned}$$

∴ The answer is 0.875

We have:

$$\begin{aligned}\phantom{=} \frac{37}{40} = \frac{37 \times 25}{40 \times 25} \quad \text{[Multiplying by 25 to get denominator 1000]} \\[1em] = \frac{925}{1000} \\[1em] = 0.925\end{aligned}$$

∴ The answer is 0.925

First, we convert the mixed fraction into an improper fraction:

$\phantom{=} 4\frac{3}{8} = \frac{4 \times 8 + 3}{8} = \frac{32 + 3}{8} = \frac{35}{8}$

Now, we divide 35 by 8. Since 35 is not exactly divisible by 8, we add a decimal point and zeros to continue the division:

$$\begin{array}{r} 4.375 \\ 8 \overline{) 35.000} \\ \underline{-32\phantom{.000}} \\ 30\phantom{00} \\ \underline{-24\phantom{00}} \\ 60\phantom{0} \\ \underline{-56\phantom{0}} \\ 40 \\ \underline{-40} \\ 0 \end{array}$$

$\frac{35}{8}$ = 4.375

∴ $4\frac{3}{8}$ = 4.375

First, we convert the mixed fraction into an improper fraction:

$\phantom{=} 9\frac{1}{25} = \frac{9 \times 25 + 1}{25} = \frac{225 + 1}{25} = \frac{226}{25}$

Now, we divide 226 by 25. Since 226 is not exactly divisible by 25, we add a decimal point and zeros to continue the division:

$$\begin{array}{r} 9.04 \\ 25 \overline{) 226.00} \\ \underline{-225\phantom{00}} \\ 100 \\ \underline{-100} \\ 0 \end{array}$$

$\frac{226}{25}$ = 9.04

∴ $9\frac{1}{25}$ = 9.04

First, we convert the mixed fraction into an improper fraction:

$\phantom{=} 2\frac{9}{16} = \frac{2 \times 16 + 9}{16} = \frac{32 + 9}{16} = \frac{41}{16}$

Now, we divide 41 by 16. We add a decimal point and zeros to continue the division:

$$\begin{array}{r} 2.5625 \\ 16 \overline{) 41.0000} \\ \underline{-32\phantom{.0000}} \\ 90\phantom{000} \\ \underline{-80\phantom{000}} \\ 100\phantom{00} \\ \underline{-096\phantom{00}} \\ 40\phantom{0} \\ \underline{-32\phantom{0}} \\ 80 \\ \underline{-80} \\ 0 \end{array}$$

$\frac{41}{16}$ = 2.5625

∴ $2\frac{9}{16}$ = 2.5625

First, we convert the mixed fraction into an improper fraction:

$4\frac{11}{125} = \frac{4 \times 125 + 11}{125} = \frac{500 + 11}{125} = \frac{511}{125}$

Now, we divide 511 by 125. We add a decimal point and zeros to continue the division:

$$\begin{array}{r} 4.088 \\ 125 \overline{) 511.000} \\ \underline{-500\phantom{.000}} \\ 1100\phantom{0} \\ \underline{-1000\phantom{0}} \\ 1000 \\ \underline{-1000} \\ 0 \end{array}$$

$\frac{511}{125}$ = 4.088

∴ $4\frac{11}{125}$ = 4.088

The maximum number of decimal places is 2. The numbers are already like decimals.

On adding column-wise, we get:

$$\begin{array}{r} 9.67 \\ +\phantom{0}15.98 \\ \hline 25.65 \\ \hline \end{array}$$

Hence, the sum is 25.65

Maximum number of decimal places in given decimals is 2. So, we convert them into like decimals, each having 2 places of decimal, by annexing zeros.

$$\begin{array}{r} 6.90 \\ +\phantom{0}23.84 \\ \hline 30.74 \\ \hline \end{array}$$

Hence, the sum is 30.74

Maximum number of decimal places in given decimals is 3. So, we convert them into like decimals, each having 3 places of decimal, by annexing zeros.

Thus, we get: 35.670, 18.794, 4.900 and 31.820

On adding column-wise, we get:

$$\begin{array}{r} 35.670 \\ 18.794 \\ 4.900 \\ +\phantom{0}31.820 \\ \hline 91.184 \\ \hline \end{array}$$

Hence, the sum is 91.184

Maximum number of decimal places in given decimals is 3. So, we convert them into like decimals, each having 3 places of decimal, by annexing zeros.

Thus, we get: 63.050, 24.839, 3.700 and 16.850

On adding column-wise, we get:

$$\begin{array}{r} 63.050 \\ 24.839 \\ 3.700 \\ +\phantom{0}16.850 \\ \hline 108.439 \\ \hline \end{array}$$

Hence, the sum is 108.439

Converting the given decimals into like decimals, we have to subtract 2.975 from 8.230.

Subtracting columnwise, we get:

$$\begin{array}{r} 8.230 \\ -\phantom{0}2.975 \\ \hline 5.255 \\ \hline \end{array}$$

Hence, the answer is 5.255

Converting the given decimals into like decimals, we have to subtract 0.75 from 1.30.

Subtracting columnwise, we get:

$$\begin{array}{r} 1.30 \\ -\phantom{0}0.75 \\ \hline 0.55 \\ \hline \end{array}$$

Hence, the answer is 0.55

Converting the given decimals into like decimals, we have to subtract 6.054 from 11.260.

Subtracting columnwise, we get:

$$\begin{array}{r} 11.260 \\ -\phantom{0}6.054 \\ \hline 5.206 \\ \hline \end{array}$$

Hence, the answer is 5.206

Converting the given decimals into like decimals, we have to subtract 134.68 from 201.30.

Subtracting columnwise, we get:

$$\begin{array}{r} 201.30 \\ -134.68 \\ \hline 66.62 \\ \hline \end{array}$$

Hence, the answer is 66.62

Converting the given decimals into like decimals, we have to subtract 6.345 from 8.100.

Subtracting columnwise, we get:

$$\begin{array}{r} 8.100 \\ -\phantom{0}6.345 \\ \hline 1.755 \\ \hline \end{array}$$

Hence, the answer is 1.755

Converting the given decimals into like decimals, we have to subtract 0.685 from 68.500.

Subtracting columnwise, we get:

$$\begin{array}{r} 68.500 \\ -\phantom{0}0.685 \\ \hline 67.815 \\ \hline \end{array}$$

Hence, the answer is 67.815

Converting the given decimals into like decimals, we have to subtract 53.865 from 90.000.

Subtracting columnwise, we get:

$$\begin{array}{r} 90.000 \\ -53.865 \\ \hline 36.135 \\ \hline \end{array}$$

Hence, the answer is 36.135

Let the required number be x

50 - x = 34.57

x = 50 - 34.57

Converting the given decimals into like decimals, we have to subtract 34.57 from 50.00.

Subtracting columnwise, we get:

$$\begin{array}{r} 50.00 \\ -34.57 \\ \hline 15.43 \\ \hline \end{array}$$

Hence, the answer is 15.43

Let the required number be x

63.47 + x = 91

x = 91 - 63.47

Converting the given decimals into like decimals, we have to subtract 63.47 from 91.00.

Subtracting columnwise, we get:

$$\begin{array}{r} 91.00 \\ -63.47 \\ \hline 27.53 \\ \hline \end{array}$$

Hence, the answer is 27.53

Given:

Total money = ₹20.00

Cost of ticket = ₹8.75

Money received back = ?

∴ Money received back = (Total money) - (Cost of ticket)

Substituting the values in above, we get:

Money received back = ₹20.00 - ₹8.75

Converting the given decimals into like decimals, we have to subtract 8.75 from 20.00.

Subtracting columnwise, we get:

$$\begin{array}{r} 20.00 \\ -\phantom{0}8.75 \\ \hline 11.25 \\ \hline \end{array}$$

Hence, he gets back ₹11.25

Given:

New weight = 6.16 kg

Previous weight = 5.58 kg

Weight gained = ?

∴ Weight gained = (New weight) - (Previous weight)

Substituting the values in above, we get:

Weight gained = 6.16 kg - 5.58 kg

Subtracting columnwise, we get:

$$\begin{array}{r} 6.16 \\ -5.58 \\ \hline 0.58 \\ \hline \end{array}$$

Hence, the baby has gained 0.58 kg

Given expression:

= 67 + 13.85 - 29.904
= 67.000 + 13.850 - 29.904 $\quad$ [Converting into like decimals]
= (67.000 + 13.850) - 29.904
= 80.850 - 29.904
= 50.546

$$\begin{array}{r|r} 67.000 & 80.850 \\ +\phantom{0}13.850 & -\phantom{0}29.904 \\ \hline 80.850 & 50.946 \\ \hline \end{array}$$

Hence, the answer is 50.946

Given expression:

= 16.753 + 4.06 - 13.89
= 16.753 + 4.060 - 13.890 $\quad$ [Converting into like decimals]
= (16.753 + 4.060) - 13.890
= 20.813 - 13.890
= 6.923

$$\begin{array}{r|r} 16.753 & 20.813 \\ +\phantom{0}4.060 & -\phantom{0}13.890 \\ \hline 20.813 & 6.923 \\ \hline \end{array}$$

Hence, the answer is 6.923

Given expression:

= 1 - 10.5 + 12.213
= 1.000 - 10.500 + 12.213 $\quad$ [Converting into like decimals]
= (1.000 + 12.213) - 10.500 $\quad$ [Rearranging terms]
= 13.213 - 10.500
= 2.713

$$\begin{array}{r|r} 1.000 & 13.213 \\ +\phantom{0}12.213 & -\phantom{0}10.500 \\ \hline 13.213 & 2.713 \\ \hline \end{array}$$

Hence, the answer is 2.713

Given expression:

= 81 - 15.68 - 4.2
= 81.00 - 15.68 - 4.20 $\quad$ [Converting into like decimals]
= (81.00) - (15.68 + 4.20) $\quad$ [Rearranging terms]
= 81.00 - 19.88
= 61.12

$$\begin{array}{r|r} 15.68 & 81.00 \\ +\phantom{0}4.20 & -\phantom{0}19.88 \\ \hline 19.88 & 61.12 \\ \hline \end{array}$$

Hence, the answer is 61.12

Given expression:

= 555 - 55.5 - 5.555
= 555.000 - 55.500 - 5.555 $\quad$ [Converting into like decimals]
= 555.000 - (55.500 + 5.555) $\quad$ [Rearranging terms]
= 555.000 - 61.055
= 493.945

$$\begin{array}{r|r} 55.500 & 555.000 \\ +\phantom{0}5.555 & -\phantom{0}61.055 \\ \hline 61.055 & 493.945 \\ \hline \end{array}$$

Hence, the answer is 493.945

Given expression:

= 100 - 32.5 - 46.74 - 12.925
= 100.000 - 32.500 - 46.740 - 12.925 $\quad$ [Converting into like decimals]
= 100.000 - (32.500 + 46.740 + 12.925) $\quad$ [Rearranging terms]
= 100.000 - 92.165
= 7.835

$$\begin{array}{r|r|r} 32.500 & 79.240 & 100.000 \\ +\phantom{0}46.740 & +\phantom{0}12.925 & -\phantom{0}92.165 \\ \hline 79.240 & 92.165 & \phantom{0}7.835 \\ \hline \end{array}$$

Hence, the answer is 7.835

We have:

6.5 x 10

On multiplying 6.5 by 10, the decimal point is shifted by one place to the right.

∴ 6.5 × 10 = 65

We have:

0.8 x 10

On multiplying 0.8 by 10, the decimal point is shifted by one place to the right.

∴ 0.8 × 10 = 8

We have:

9.07 x 10

On multiplying 9.07 by 10, the decimal point is shifted by one place to the right.

∴ 9.07 × 10 = 90.7

We have:

2.345 x 10

On multiplying 2.345 by 10, the decimal point is shifted by one place to the right.

∴ 2.345 × 10 = 23.45

We have:

4.63 x 100

On multiplying 4.63 by 100, the decimal point is shifted by two places to the right.

∴ 4.63 × 100 = 463

We have:

8.279 x 100

On multiplying 8.279 by 100, the decimal point is shifted by two places to the right.

∴ 8.279 × 100 = 827.9

We have:

7.8 x 100

On multiplying 7.8 by 100, the decimal point is shifted by two places to the right.

∴ 7.8 × 100 = 780

We have:

0.09 x 100

On multiplying 0.09 by 100, the decimal point is shifted by two places to the right.

∴ 0.09 × 100 = 9

We have:

0.283 x 1000

On multiplying 0.283 by 1000, the decimal point is shifted by three places to the right.

∴ 0.283 × 1000 = 283

We have:

6.25 x 1000

On multiplying 6.25 by 1000, the decimal point is shifted by three places to the right.

∴ 6.25 × 1000 = 6250

We have:

5.4 x 1000

On multiplying 5.4 by 1000, the decimal point is shifted by three places to the right.

∴ 5.4 × 1000 = 5400

We have:

0.3 x 1000

On multiplying 0.3 by 1000, the decimal point is shifted by three places to the right.

∴ 0.3 × 1000 = 300

We have:

24 x 16 = 384

∴ 2.4 × 16 = 38.4 $\quad$ [1 place of decimal]

The answer is 38.4

We have:

345 × 17 = 5865

∴ 3.45 × 17 = 58.65 $\quad$ [2 places of decimal]

The answer is 58.65

We have:

86 × 14 = 1204

∴ 0.86 × 14 = 12.04 $\quad$ [2 places of decimal]

The answer is 12.04

We have:

268 × 30 = 8040

∴ 2.68 × 30 = 80.4 $\quad$ [2 places of decimal]

The answer is 80.4

We have:

23 × 65 = 1495

∴ 0.023 × 65 = 1.495 $\quad$ [3 places of decimal]

The answer is 1.495

We have:

6 × 15 = 90

∴ 0.0006 × 15 = 0.009 $\quad$ [4 places of decimal]

The answer is 0.009

First we multiply 56 by 14

$$\begin{matrix} & & 5 & 6 \\ \times & & 1 & 4 \\ \hline & 2 & 2 & 4 \\ & 5 & 6 & \times \\ \hline & \bold{7} & \bold{8} & \bold{4} \end{matrix}$$

Clearly, 56 × 14 = 784

Sum of decimal places in given decimals = (1 + 1) = 2

So, the product contains 2 places of decimal

∴ 5.6 × 1.4 = 7.84

First we multiply 235 by 72

$$\begin{matrix} & & 2 & 3 & 5 \\ \times & & & 7 & 2 \\ \hline & & 4 & 7 & 0 \\ 1 & 6 & 4 & 5 & \times \\ \hline \bold{1} & \bold{6} & \bold{9} & \bold{2} & \bold{0} \end{matrix}$$

Clearly, 235 × 72 = 16920

Sum of decimal places in given decimals = (2 + 1) = 3

So, the product contains 3 places of decimal

∴ 2.35 × 7.2 = 16.920 = 16.92

First we multiply 37 by 26

$$\begin{matrix} & & 3 & 7 \\ \times & & 2 & 6 \\ \hline & 2 & 2 & 2 \\ & 7 & 4 & \times \\ \hline & \bold{9} & \bold{6} & \bold{2} \end{matrix}$$

Clearly, 37 × 26 = 962

Sum of decimal places in given decimals = (2 + 2) = 4

So, the product contains 4 places of decimal

∴ 0.37 × 0.26 = 0.0962

First we multiply 74 by 67

$$\begin{matrix} & & & 7 & 4 \\ \times & & & 6 & 7 \\ \hline & & 5 & 1 & 8 \\ & 4 & 4 & 4 & \times \\ \hline & \bold{4} & \bold{9} & \bold{5} & \bold{8} \end{matrix}$$

Clearly, 74 × 67 = 4958

Sum of decimal places in given decimals = (2 + 1) = 3

So, the product contains 3 places of decimal

∴ 0.74 × 6.7 = 4.958

First we multiply 564 by 8

$$\begin{matrix} & & 5 & 6 & 4 \\ \times & & & & 8 \\ \hline & \bold{4} & \bold{5} & \bold{1} & \bold{2} \end{matrix}$$

Clearly, 564 × 8 = 4512

Sum of decimal places in given decimals = (2 + 2) = 4

So, the product contains 4 places of decimal

∴ 5.64 × 0.08 = 0.4512

First we multiply 275 by 17

$$\begin{matrix} & & 2 & 7 & 5 \\ \times & & & 1 & 7 \\ \hline & 1 & 9 & 2 & 5 \\ & 2 & 7 & 5 & \times \\ \hline & \bold{4} & \bold{6} & \bold{7} & \bold{5} \end{matrix}$$

Clearly, 275 × 17 = 4675

Sum of decimal places in given decimals = (2 + 1) = 3

So, the product contains 3 places of decimal

∴ 2.75 × 1.7 = 4.675

First we multiply 4 by 36

$$\begin{matrix} & & 3 & 6 \\ \times & & & 4 \\ \hline & \bold{1} & \bold{4} & \bold{4} \end{matrix}$$

Clearly, 4 × 36 = 144

Sum of decimal places in given decimals = (2 + 2) = 4

So, the product contains 4 places of decimal

∴ 0.04 × 0.36 = 0.0144

First we multiply 342 by 186

$$\begin{matrix} & & 3 & 4 & 2 \\ \times & & 1 & 8 & 6 \\ \hline & 2 & 0 & 5 & 2 \\ 2 & 7 & 3 & 6 & \times \\ 3 & 4 & 2 & \times & \times \\ \hline \bold{6} & \bold{3} & \bold{6} & \bold{1} & \bold{2} \end{matrix}$$

Clearly, 342 × 186 = 63612

Sum of decimal places in given decimals = (1 + 2) = 3

So, the product contains 3 places of decimal

∴ 34.2 × 1.86 = 63.612

First we multiply 28 by 9

$$\begin{matrix} & & 2 & 8 \\ \times & & & 9 \\ \hline & \bold{2} & \bold{5} & \bold{2} \end{matrix}$$

Clearly, 28 × 9 = 252

Sum of decimal places in given decimals = (3 + 1) = 4

So, the product contains 4 places of decimal

∴ 0.028 × 0.9 = 0.0252

First we multiply 23 by 23 and then by 1

$$\begin{matrix} & & 2 & 3 \\ \times & & 2 & 3 \\ \hline & & 6 & 9 \\ & 4 & 6 & \times \\ \hline & \bold{5} & \bold{2} & \bold{9} \end{matrix}$$

Clearly, 23 × 23 × 1 = 529

Sum of decimal places in given decimals = (1 + 2 + 1) = 4

So, the product contains 4 places of decimal

529 x 1 = 529

∴ 2.3 × 0.23 × 0.1 = 0.0529

First we multiply 12 by 35 and then by 3

$$\begin{matrix} & & 1 & 2 \\ \times & & 3 & 5 \\ \hline & & 6 & 0 \\ & 3 & 6 & \times \\ \hline & \bold{4} & \bold{2} & \bold{0} \end{matrix}$$

∴ 12 × 35 = 420

$$\begin{matrix} & & 4 & 2 & 0 \\ \times & & & & 3 \\ \hline & \bold{1} & \bold{2} & \bold{6} & \bold{0} \end{matrix}$$

∴ 12 × 35 × 3 = 1260

Sum of decimal places in given decimals = (1 + 1 + 1) = 3

So, the product contains 3 places of decimal

∴ 1.2 × 3.5 × 0.3 = 1.260 = 1.26

First we multiply 6 by 15 and then by 7

$$\begin{matrix} & 1 & 5 \\ \times & & 6 \\ \hline & \bold{9} & \bold{0} \end{matrix}$$

∴ 6 × 15 = 90

$$\begin{matrix} & 9 & 0 \\ \times & & 7 \\ \hline \bold{6} & \bold{3} & \bold{0} \end{matrix}$$

∴ 6 × 15 x 7 = 630

Sum of decimal places in given decimals = (1 + 1 + 1) = 3

So, the product contains 3 places of decimal

∴ 0.6 × 1.5 × 0.7 = 0.630 = 0.63

First we multiply 2 by 2 and then by 2

$$\begin{matrix} & 2 \\ \times & 2 \\ \hline & \bold{4} \end{matrix}$$

∴ 2 × 2 = 4

$$\begin{matrix} & 4 \\ \times & 2 \\ \hline & \bold{8} \end{matrix}$$

∴ 2 × 2 x 2 = 8

Sum of decimal places in given decimals = (1 + 1 + 2) = 4

So, the product contains 4 places of decimal

∴ 0.2 × 0.2 × 0.02 = 0.0008

First we multiply 11 by 1 and then by 11

$$\begin{matrix} & 1 & 1 \\ \times & & 1 \\ \hline & \bold{1} & \bold{1} \end{matrix}$$

∴ 11 × 1 = 11

$$\begin{matrix} & & 1 & 1 \\ \times & & 1 & 1 \\ \hline & & 1 & 1 \\ & 1 & 1 & \times \\ \hline & \bold{1} & \bold{2} & \bold{1} \end{matrix}$$

∴ 11 × 1 x 11 = 121

Sum of decimal places in given decimals = (1 + 1 + 2) = 4

So, the product contains 4 places of decimal

∴ 1.1 × 0.1 × 0.11 = 0.0121

First we multiply 6 by 6 and then by 6

$$\begin{matrix} & & 6 \\ \times & & 6 \\ \hline & \bold{3} & \bold{6} \end{matrix}$$

∴ 6 × 6 = 36

$$\begin{matrix} & 3 & 6 \\ \times & & 6 \\ \hline \bold{2} & \bold{1} & \bold{6} \end{matrix}$$

∴ 6 × 6 × 6 = 216

Sum of decimal places in given decimals = (1 + 2 + 3) = 6

So, the product contains 6 places of decimal

∴ 0.6 × 0.06 × 0.006 = 0.000216

We have:

(1.3)² = 1.3 × 1.3

First we multiply 13 by 13

$$\begin{matrix} & & 1 & 3 \\ \times & & 1 & 3 \\ \hline & & 3 & 9 \\ & 1 & 3 & \times \\ \hline & \bold{1} & \bold{6} & \bold{9} \end{matrix}$$

∴ 13 × 13 = 169

Sum of decimal places in given decimals = (1 + 1) = 2

So, the product contains 2 places of decimal

∴ (1.3)² = 1.69

We have:

(0.06)² = 0.06 × 0.06

First we multiply 6 by 6

$$\begin{matrix} & & 6 \\ \times & & 6 \\ \hline & \bold{3} & \bold{6} \end{matrix}$$

∴ 6 × 6 = 36

Sum of decimal places in given decimals = (2 + 2) = 4

So, the product contains 4 places of decimal

∴ (0.06)² = 0.0036

We have:

(0.2)³ = 0.2 × 0.2 × 0.2

First we multiply 2 × 2 × 2

$$\begin{matrix} & 2 \\ \times & 2 \\ \hline & \bold{4} \end{matrix}$$

∴ 2 × 2 =4

$$\begin{matrix} & 4 \\ \times & 2 \\ \hline & \bold{8} \end{matrix}$$

∴ 2 × 2 × 2 = 8

Sum of decimal places in given decimals = (1 + 1 + 1) = 3

So, the product contains 3 places of decimal

∴ (0.2)³ = 0.008

We have:

(0.8)³ = 0.8 × 0.8 × 0.8

First we multiply 8 × 8 × 8

$$\begin{matrix} & & 8 \\ \times & & 8 \\ \hline & \bold{6} & \bold{4} \end{matrix}$$

∴ 8 × 8 = 64

$$\begin{matrix} & 6 & 4 \\ \times & & 8 \\ \hline \bold{5} & \bold{1} & \bold{2} \end{matrix}$$

∴ 8 × 8 × 8 = 512

Sum of decimal places in given decimals = (1 + 1 + 1) = 3

So, the product contains 3 places of decimal

∴ (0.8)³ = 0.512

Given:

Cost of 1 pen = ₹42.25

Number of pens = 1 dozen = 12 pens

The cost of 1 dozen pens = (Cost of 1 pen) x (Number of pens)

Substituting the values in above, we get:

The cost of 1 dozen pens = ₹42.25 x 12

Sum of the decimal places in given decimals = 2 + 0 = 2

So, the product contains 2 places of decimal.

$$\begin{matrix} & & 4 & 2 & 2 & 5 \\ \times & & & & 1 & 2 \\ \hline & & 8 & 4 & 5 & 0 \\ & 4 & 2 & 2 & 5 & \times \\ \hline & \bold{5} & \bold{0} & \bold{7} & \bold{0} & \bold{0} \end{matrix}$$

∴ ₹42.25 × 12 = ₹507.00 = ₹507

Hence, the cost of one dozen pens = ₹507

Given:

Speed per hour = 56.4 km

Total time = 3.5 hours

Distance covered = ?

We know the formula,

Distance = Speed x Time

Substituting the values in above, we get:

Distance = 56.4 km x 3.5 hours

Sum of the decimal places in given decimals = 1 + 1 = 2

So, the product contains 2 places of decimal

$$\begin{matrix} & & 5 & 6 & 4 \\ \times & & & 3 & 5 \\ \hline & 2 & 8 & 2 & 0 \\ 1 & 6 & 9 & 2 & \times \\ \hline \bold{1} & \bold{9} & \bold{7} & \bold{4} & \bold{0} \end{matrix}$$

∴ 56.4 km × 3.5 hours = 197.40 km = 197.4 km

Hence, the distance covered by the car = 197.4 km

Given:

Length of the room = 4.5 m

Breadth of the room = 3.8 m

Area of the floor = ?

The floor will be of rectangular shape

We know the formula,

Area = Length x Breadth

Substituting the values in above, we get:

Area = 4.5 m x 3.8 m

Sum of the decimal places in given decimals = 1 + 1 = 2

So, the product contains 2 places of decimal

$$\begin{matrix} & & 4 & 5 \\ \times & & 3 & 8 \\ \hline & 3 & 6 & 0 \\ 1 & 3 & 5 & \times \\ \hline \bold{1} & \bold{7} & \bold{1} & \bold{0} \end{matrix}$$

∴ 4.5 m × 3.8 m = 17.10 m² = 17.1 m²

Hence, the area of the floor = 17.1 m²

Given:

Cost of 1 litre of refined oil = ₹124.75

Total quantity of oil = 6.2 litres

Cost of 6.2 litres of oil = ?

Cost of 6.2 litres of oil = (Cost of 1 litre) x (Total quantity)

Substituting the values in above, we get:

Cost of 6.2 litres of oil = (₹124.75) x (6.2 litres)

Sum of the decimal places in given decimals = 2 + 1 = 3

So, the product contains 3 places of decimal

$$\begin{matrix} & & 1 & 2 & 4 & 7 & 5 \\ \times & & & & & 6 & 2 \\ \hline & & 2 & 4 & 9 & 5 & 0 \\ & 7 & 4 & 8 & 5 & 0 & \times \\ \hline & \bold{7} & \bold{7} & \bold{3} & \bold{4} & \bold{5} & \bold{0} \end{matrix}$$

∴ 124.75 × 6.2 litres = ₹773.450 = ₹773.45

Hence, the cost of 6.2 litres of oil = ₹773.45

On dividing 2.8 by 10, the decimal point is shifted by one place to the left.

∴ 2.8 ÷ 10 = 0.28

On dividing 0.63 by 10, the decimal point is shifted by one place to the left.

∴ 0.63 ÷ 10 = 0.063

On dividing 3.05 by 10, the decimal point is shifted by one place to the left.

∴ 3.05 ÷ 10 = 0.305

On dividing 245.6 by 100, the decimal point is shifted by two places to the left.

∴ 245.6 ÷ 100 = 2.456

On dividing 0.9 by 100, the decimal point is shifted by two places to the left.

∴ 0.9 ÷ 100 = 0.009

On dividing 1.23 by 100, the decimal point is shifted by two place to the left.

∴ 1.23 ÷ 10 = 0.0123

On dividing 134.2 by 1000, the decimal point is shifted by three places to the left.

∴ 134.2 ÷ 1000 = 0.1342

On dividing 23.4 by 1000, the decimal point is shifted by three places to the left.

∴ 23.4 ÷ 1000 = 0.0234

On dividing 0.7 by 1000, the decimal point is shifted by three places to the left.

∴ 0.7 ÷ 1000 = 0.0007

On dividing 20.79 by 9, we get:

$$\begin{array}{r} 2.31 \\ 9 \overline{\smash{)} 20.79 } \\ \underline{18}\phantom{.00} \\ 27\phantom{0} \\ \underline{27}\phantom{0} \\ 09 \\ \underline{09} \\ 0 \phantom{.} \end{array}$$

Hence, 20.79 ÷ 9 = 2.31

On dividing 78.48 by 12, we get:

$$\begin{array}{r} 6.54 \\ 12 \overline{\smash{)} 78.48 } \\ \underline{72}\phantom{.00} \\ 64\phantom{0} \\ \underline{60}\phantom{0} \\ 048 \\ \underline{048} \\ 0 \phantom{.} \end{array}$$

Hence, 78.48 ÷ 12 = 6.54

On dividing 142.8 by 21, we get:

$$\begin{array}{r} 6.8 \\ 21 \overline{\smash{)} 142.8 } \\ \underline{126}\phantom{.0} \\ 168 \\ \underline{168} \\ 0 \phantom{.} \end{array}$$

Hence, 142.8 ÷ 21 = 6.8

On dividing 6.02 by 7, we get:

$$\begin{array}{r} 0.86 \\ 7 \overline{\smash{)} 6.02 } \\ \underline{0}\phantom{.00} \\ 60\phantom{1} \\ \underline{56}\phantom{0} \\ 042 \\ \underline{042} \\ 0 \phantom{.} \end{array}$$

Hence, 6.02 ÷ 7 = 0.86

On dividing 0.688 by 8, we get:

$$\begin{array}{r} 0.086 \\ 8 \overline{\smash{)} 0.688 } \\ \underline{0}\phantom{.000} \\ 68\phantom{0} \\ \underline{64}\phantom{0} \\ 48 \\ \underline{48} \\ 0 \phantom{.} \end{array}$$

Hence, 0.688 ÷ 8 = 0.086

On dividing 0.125 by 25, we get:

$$\begin{array}{r} 0.005 \\ 25 \overline{\smash{)} 0.125 } \\ \underline{0}\phantom{.000} \\ 125 \\ \underline{125} \\ 0 \phantom{.} \end{array}$$

Hence, 0.125 ÷ 25 = 0.005

On dividing 0.992 by 31, we get:

$$\begin{array}{r} 0.032 \\ 31 \overline{\smash{)} 0.992 } \\ \underline{0}\phantom{.000} \\ 99\phantom{0} \\ \underline{93}\phantom{0} \\ 62 \\ \underline{62} \\ 0 \phantom{.} \end{array}$$

Hence, 0.992 ÷ 31 = 0.032

On dividing 0.1728 by 72, we get:

$$\begin{array}{r} 0.0024 \\ 72 \overline{\smash{)} 0.1728 } \\ \underline{0}\phantom{.0000} \\ 172\phantom{0} \\ \underline{144}\phantom{0} \\ 288 \\ \underline{288} \\ 0 \phantom{.} \end{array}$$

Hence, 0.1728 ÷ 72 = 0.0024

On dividing 0.12749 by 61, we get:

$$\begin{array}{r} 0.00209 \\ 61 \overline{\smash{)} 0.12749 } \\ \underline{0}\phantom{.00000} \\ 127\phantom{00} \\ \underline{122}\phantom{00} \\ 549 \\ \underline{549} \\ 0 \phantom{.} \end{array}$$

Hence, 0.12749 ÷ 61 = 0.00209

We have:

$\frac{2.24}{0.8} = \frac{2.24 \times 10}{0.8 \times 10} = \frac{22.4}{8}$

On dividing 22.4 by 8, we get:

$$\begin{array}{r} 2.8 \\ 8 \overline{\smash{)} 22.4 } \\ \underline{16}\phantom{.0} \\ 64 \\ \underline{64} \\ 0 \phantom{.} \end{array}$$

Hence, $\frac{2.24}{0.8} = \frac{22.4}{8} = 2.8$

We have:

$\frac{1.242}{1.8} = \frac{1.242 \times 10}{1.8 \times 10} = \frac{12.42}{18}$

On dividing 12.42 by 18, we get:

$$\begin{array}{r} 0.69 \\ 18 \overline{\smash{)} 12.42 } \\ \underline{108\phantom{0}} \\ 162 \\ \underline{162} \\ 0 \phantom{.} \end{array}$$

Hence, $\frac{1.242}{1.8} = \frac{12.42}{18} = 0.69$

We have:

$\frac{0.1575}{0.21} = \frac{0.1575 \times 100}{0.21 \times 100} = \frac{15.75}{21}$

On dividing 15.75 by 21, we get:

$$\begin{array}{r} 0.75 \\ 21 \overline{\smash{)} 15.75 } \\ \underline{147\phantom{0}} \\ 105 \\ \underline{105} \\ 0 \phantom{.} \end{array}$$

Hence, $\frac{0.1575}{0.21} = \frac{15.75}{21} = 0.75$

We have:

$\frac{0.0144}{0.12} = \frac{0.0144 \times 100}{0.12 \times 100} = \frac{1.44}{12}$.

On dividing 1.44 by 12, we get:

$$\begin{array}{r} 0.12 \\ 12 \overline{\smash{)} 1.44 } \\ \underline{12\phantom{0}} \\ 024 \\ \underline{024} \\ 0 \phantom{.} \end{array}$$

Hence, $\frac{0.0144}{0.12} = \frac{1.44}{12} = 0.12$

We have:

$\frac{0.0783}{0.9} = \frac{0.0783 \times 10}{0.9 \times 10} = \frac{0.783}{9}$

On dividing 0.783 by 9, we get:

$$\begin{array}{r} 0.087 \\ 9 \overline{\smash{)} 0.783 } \\ \underline{0.72}\phantom{0} \\ 0.063 \\ \underline{0.063} \\ 0 \phantom{.} \end{array}$$

Hence, $\frac{0.0783}{0.9} = \frac{0.783}{9} = 0.087$

We have:

$\frac{0.1164}{0.012} = \frac{0.1164 \times 1000}{0.012 \times 1000} = \frac{116.4}{12}$.

On dividing 116.4 by 12, we get:

$$\begin{array}{r} 9.7 \\ 12 \overline{\smash{)} 116.4 } \\ \underline{108}\phantom{.0} \\ 84 \\ \underline{84} \\ 0 \phantom{.} \end{array}$$

Hence, $\frac{0.1164}{0.012} = \frac{116.4}{12} = 9.7$

We have:

$\frac{0.068}{0.17} = \frac{0.068 \times 100}{0.17 \times 100} = \frac{6.8}{17}$.

On dividing 6.8 by 17, we get:

$$\begin{array}{r} 0.4 \\ 17 \overline{\smash{)} 6.8 } \\ \underline{0}\phantom{.8} \\ 68 \phantom{.} \\ \underline{68} \phantom{.} \\ 0 \phantom{0} \end{array}$$

Hence, $\frac{0.068}{0.17} = \frac{6.8}{17} = 0.4$

We have:

$\frac{0.02324}{0.28} = \frac{0.02324 \times 100}{0.28 \times 100} = \frac{2.324}{28}$.

On dividing 2.324 by 28, we get:

$$\begin{array}{r} 0.083 \\ 28 \overline{\smash{)} 2.324 } \\ \underline{224\phantom{0}} \\ 84 \\ \underline{84} \\ 0 \phantom{.} \end{array}$$

Hence, $\frac{0.02324}{0.28} = \frac{2.324}{28} = 0.083$

We have:

$\frac{0.03822}{0.049} = \frac{0.03822 \times 1000}{0.049 \times 1000} = \frac{38.22}{49}$.

On dividing 38.22 by 49, we get:

$$\begin{array}{r} 0.78 \\ 49 \overline{\smash{)} 38.22 } \\ \underline{343} \phantom{0} \\ 392 \\ \underline{392} \\ 0 \phantom{.} \end{array}$$

Hence, $\frac{0.03822}{0.049} = \frac{38.22}{49} = 0.78$

We have:

$\phantom{=} \frac{1.3 \times 2.4}{0.39} = \frac{3.12}{0.39} = \frac{3.12 \times 100}{0.39 \times 100} = \frac{312}{39}$

On dividing 312 by 39, we get:

$$\begin{array}{r} 8 \\ 39 \overline{\smash{)} 312 } \\ \underline{312} \\ 0 \end{array}$$

Hence, the answer is 8.

We have:

$\phantom{=} \frac{2.5 \times 40.4}{50} = \frac{101.0}{50} = \frac{101}{50}$

On dividing 101 by 50, we get:

$$\begin{array}{r} 2.02 \\ 50 \overline{\smash{)} 101.00 } \\ \underline{100} \phantom{.00} \\ 10 \phantom{0} \\ \underline{00} \phantom{0} \\ 100 \\ \underline{100} \\ 0 \end{array}$$

Hence, the answer is 2.02

We have:

$\frac{6.3}{0.03} = \frac{6.3 \times 100}{0.03 \times 100} = \frac{630}{3}$

On dividing 630 by 3, we get:

$$\begin{array}{r} 210 \\ 3 \overline{\smash{)} 630 } \\ \underline{6} \phantom{00} \\ 03 \phantom{0} \\ \underline{3} \phantom{0} \\ 00 \\ \underline{0} \\ 0 \end{array}$$

Hence, the answer is 210

Given:

Cost of 8 pencils = ₹46.80

Number of pencils = 8

Cost of each pencil = ?

Cost of each pencil = (Total Cost) ÷ (Number of pencils)

Substituting the values:

Cost of each pencil = ₹46.80 ÷ 8

On dividing 46.80 by 8, we get:

$$\begin{array}{r} 5.85 \\ 8 \overline{\smash{)} 46.80 } \\ \underline{40} \phantom{.00} \\ 68 \phantom{0} \\ \underline{64} \phantom{0} \\ 040 \\ \underline{040} \\ 0 \end{array}$$

46.80 ÷ 8 = 5.85

Hence, the cost of each pencil is ₹5.85

Given:

Distance = 276.75 km

Time = 4.5 hours

Speed = ?

We know the formula,

Speed = Distance ÷ Time

Substituting the values:

Speed = 276.75 km ÷ 4.5 hours

= $\frac{276.75 \times 10}{4.5 \times 10}$

= $\frac{2767.5}{45} \quad$ [Multiplying both sides by 10 to make denominator a whole number]

On dividing 2767.5 by 45, we get:

$$\begin{array}{r} 61.5 \\ 45 \overline{\smash{)} 2767.5 } \\ \underline{270} \phantom{.00} \\ 67 \phantom{.0} \\ \underline{45} \phantom{.0} \\ 225 \\ \underline{225} \\ 0 \phantom{0} \end{array}$$

276.75 ÷ 4.5 = 61.5

Hence, the average speed of the car is 61.5 km/h

Given:

Total Cost = ₹326.25

Total length = 2.25 m

Cost of 1 m cloth = ?

Cost of 1 m cloth = (Total Cost) ÷ (Total length)

Substituting the values:

Cost of 1 m cloth = ₹326.25 ÷ 2.25 m

= $\frac{326.25 \times 100}{2.25 \times 100}$

= $\frac{32625}{225} \quad$ [Multiplying both sides by 100 to make denominator a whole number]

On dividing 32625 by 225, we get:

$$\begin{array}{r} 145 \\ 225 \overline{\smash{)} 32625 } \\ \underline{225} \phantom{00} \\ 1012 \phantom{0} \\ \underline{900} \phantom{0} \\ 1125 \\ \underline{1125} \\ 0 \end{array}$$

326.25 ÷ 2.25 = 145

Hence, the cost of 1 m of cloth is ₹145

Let p and q be two numbers

Given:

Product of two numbers = 52.8

One number = p = 8.25

Other number = q = ?

p x q = 52.8

Substituting the values:

8.25 x q = 52.8

q = 52.8 ÷ 8.25 $\quad$ [Solving for q]

= $\frac{52.8 \times 100}{8.25 \times 100}$

= $\frac{5280}{825} \quad$ [Multiplying both sides by 100 to make denominator a whole number]

On dividing 5280 by 825, we get:

$$\begin{array}{r} 6.4 \\ 825 \overline{\smash{)} 5280.0 } \\ \underline{4950} \phantom{.0} \\ 330.0 \\ \underline{330.0} \\ 0 \end{array}$$

52.8 ÷ 8.25 = 6.4

Hence, the other number is 6.4

Given:

Total length of rope = 61.2 cm

Length of each piece = 3.6 cm

Number of pieces = ?

Number of pieces = (Total length) ÷ (Length of each piece)

Substituting the values:

Number of pieces = 61.2 cm ÷ 3.6 cm

$= \frac{61.2 \times 10}{3.6 \times 10} = \frac{612}{36}$

On dividing 612 by 36, we get:

$$\begin{array}{r} 17 \\ 36 \overline{\smash{)} 612 } \\ \underline{36} \phantom{0} \\ 252 \\ \underline{252} \\ 0 \end{array}$$

61.2 ÷ 3.6 = 17

Hence, 17 equal pieces can be cut from the rope.

By actual division, we get:

$$\begin{array}{r} 6.666... \\ 3 \overline{\smash{)} 20.000 } \\ \underline{18} \phantom{.000} \\ 20 \phantom{.00} \\ \underline{18} \phantom{.00} \\ 20 \phantom{.0} \\ \underline{18} \phantom{.0} \\ 2 \phantom{.} \end{array}$$

∴ $\frac{20}{3} = 6.666... = 6.\overline{6}$

By actual division, we get:

$$\begin{array}{r} 0.2727... \\ 11 \overline{\smash{)} 3.0000 } \\ \underline{22} \phantom{.000} \\ 80 \phantom{.00} \\ \underline{77} \phantom{.00} \\ 30 \phantom{.0} \\ \underline{22} \phantom{.0} \\ 80 \phantom{} \\ \underline{77} \phantom{} \\ 3 \phantom{} \end{array}$$

∴ $\frac{3}{11} = 0.2727... = 0.\overline{27}$

By actual division, we get:

$$\begin{array}{r} 0.833... \\ 6 \overline{\smash{)} 5.000 } \\ \underline{48} \phantom{.00} \\ 20 \phantom{.0} \\ \underline{18} \phantom{.0} \\ 20 \phantom{} \\ \underline{18} \phantom{} \\ 2 \phantom{} \end{array}$$

∴ $\frac{5}{6} = 0.833... = 0.8\overline{3}$

By actual division, we get:

$$\begin{array}{r} 0.188... \\ 90 \overline{\smash{)} 17.000 } \\ \underline{90} \phantom{.00} \\ 800 \phantom{.0} \\ \underline{720} \phantom{.0} \\ 800 \phantom{} \\ \underline{720} \phantom{} \\ 80 \phantom{} \end{array}$$

∴ $\frac{17}{90} = 0.188... = 0.1\overline{8}$

By actual division, we get:

$$\begin{array}{r} 0.027027... \\ 37 \overline{\smash{)} 1.000000 } \\ \underline{0} \phantom{.00000} \\ 100 \phantom{.0000} \\ \underline{74} \phantom{.0000} \\ 260 \phantom{.000} \\ \underline{259} \phantom{.000} \\ 10 \phantom{.00} \\ \underline{0} \phantom{.00} \\ 100 \phantom{.0} \\ \underline{74} \phantom{.0} \\ 26 \phantom{} \end{array}$$

∴ $\frac{1}{37} = 0.027027... = 0.\overline{027}$

By actual division, we get:

$$\begin{array}{r} 3.142857... \\ 7 \overline{\smash{)} 22.000000 } \\ \underline{21} \phantom{.00000} \\ 10 \phantom{.0000} \\ \underline{7} \phantom{.0000} \\ 30 \phantom{.000} \\ \underline{28} \phantom{.000} \\ 20 \phantom{.00} \\ \underline{14} \phantom{.00} \\ 60 \phantom{.0} \\ \underline{56} \phantom{.0} \\ 40 \phantom{} \\ \underline{35} \phantom{} \\ 50 \phantom{} \\ \underline{49} \phantom{} \\ 1 \phantom{} \end{array}$$

∴ $\frac{22}{7} = 3.14285714... = 3.\overline{142857}$

By actual division, we get:

$$\begin{array}{r} 0.153846... \\ 13 \overline{\smash{)} 2.000000 } \\ \underline{13} \phantom{.00000} \\ 70 \phantom{.0000} \\ \underline{65} \phantom{.0000} \\ 50 \phantom{.000} \\ \underline{39} \phantom{.000} \\ 110 \phantom{.00} \\ \underline{104} \phantom{.00} \\ 60 \phantom{.0} \\ \underline{52} \phantom{.0} \\ 80 \phantom{} \\ \underline{78} \phantom{} \\ 2 \phantom{} \end{array}$$

∴ $\frac{2}{13} = 0.153846153846... = 0.\overline{153846}$

Let $x = 0.\overline{6}$. Then,

x = 0.6666... (i)

⇒ 10x = 6.6666... (ii)

On subtracting (i) from (ii), we get:

$$\begin{aligned}9x = 6 \\[1em] \Rightarrow x = \frac{6}{9} = \frac{2}{3}\end{aligned}$$

Hence, $0.\overline{6} = \frac{2}{3}$

Let $x = 0.\overline{8}$. Then,

x = 0.8888... (i)

⇒ 10x = 8.8888... (ii)

On subtracting (i) from (ii), we get:

$$\begin{aligned}9x = 8 \\[1em] \Rightarrow x = \frac{8}{9}\end{aligned}$$

Hence, $0.\overline{8} = \frac{8}{9}$

Let $x = 0.\overline{34}$. Then,

x = 0.343434... (i)

⇒ 100x = 34.343434... (ii)

On subtracting (i) from (ii), we get:

$$\begin{aligned}99x = 34 \\[1em] \Rightarrow x = \frac{34}{99}\end{aligned}$$

Hence, $0.\overline{34} = \frac{34}{99}$

Let x = $2.\overline{13}$.

Then,

x = 2.131313... (i)

⇒ 100x = 213.131313... (ii)

On subtracting (i) from (ii), we get:

$$\begin{aligned}99x = 211 \\[1em] \Rightarrow x = \frac{211}{99} \\[1em] \Rightarrow x = 2\frac{13}{99}\end{aligned}$$

Hence, $2.\overline{13} = 2\frac{13}{99}$

Let $x = 1.\overline{243}$. Then,

x = 1.243243243... (i)

⇒ 1000x = 1243.243243... (ii)

On subtracting (i) from (ii), we get:

$$\begin{aligned}999x = 1242 \\[1em] \Rightarrow x = \frac{1242}{999} \\[1em] \Rightarrow x = 1\frac{243}{999} \\[1em]\end{aligned}$$

Hence, $1.\overline{243} = 1\frac{243}{999}$

Let $x = 0.1\overline{6} = 0.1666...$

Multiplying by 10 to move the non-repeating digit:

10x = 1.6666... $\qquad$..... (i)

Multiplying by 100 to move the decimal past the first repeating digit:

100x = 16.6666... $\qquad$..... (ii)

On subtracting (i) from (ii), we get:

$$\begin{aligned}90x = 15 \\[1em] \Rightarrow x = \frac{15}{90} = \frac{1}{6}\end{aligned}$$

Hence, $0.1\overline{6} = \frac{1}{6}$.

Let $x = 0.1\overline{43} = 0.1434343...$

Multiplying by 10 to move the decimal past the non-repeating digit:

10x = 1.434343... $\qquad$ ..... (i)

Multiplying by 1000 to move the decimal past the first repeating block:

1000x = 143.434343... $\qquad$ ..... (ii)

Subtracting (i) from (ii), we get:

$$\begin{aligned}990x = 142 \\[1em] \Rightarrow x = \frac{142}{990} = \frac{71}{495}\end{aligned}$$

Hence, $0.1\overline{43} = \frac{71}{495}$

Let $x = 0.57\overline{4} = 0.57444...$

Multiplying by 100 to move the decimal past the non-repeating digits:

100x = 57.444..... (i)

Multiplying by 10 to move the decimal past the first repeating block:

1000x = 574.444..... (ii)

Subtracting (i) from (ii):

$$\begin{aligned}900x = 517 \\[1em] \Rightarrow x = \frac{517}{900}\end{aligned}$$

Hence, $0.57\overline{4} = \frac{517}{900}$

Let $x = 0.12\overline{34} = 0.12343434...$

Multiplying by 100 to move the decimal past the non-repeating digits:

100x = 12.343434..... (i)

Multiplying by 100 to move the decimal past the first repeating block:

10000x = 1234.343434..... (ii)

Subtracting (i) from (ii):

$$\begin{aligned}9900x = 1222 \\[1em] \Rightarrow x = \frac{1222}{9900} = \frac{611}{4950}\end{aligned}$$

Hence, $0.12\overline{34} = \frac{611}{4950}$

The given number is 87.46. Its whole number part is 87.

First digit to the right of decimal is 4 < 5.

∴ Required rounded off number is 87.

The given number is 65.83. Its whole number part is 65.

First digit to the right of decimal is 8 > 5.

So, we increase the whole number part by 1.

∴ Required rounded off number is 66.

The given number is 71.54. Its whole number part is 71.

First digit to the right of decimal is 5.

So, we increase the whole number part by 1.

∴ Required rounded off number is 72.

The given number is 98.5. Its whole number part is 98.

First digit to the right of decimal is 5.

So, we increase the whole number part by 1.

∴ Required rounded off number is 99.

The given number is 60.29. Its whole number part is 60.

First digit to the right of decimal is 2 < 5.

∴ Required rounded off number is 60.

The given number is 6.342

This number up to 2 decimal places is 6.34

The third decimal place is 2 < 5

∴ The number correct to 2 decimal places is 6.34

The given number is 8.1347

This number up to 3 decimal places is 8.134

The fourth decimal place is 7 > 5

So, we increase the 3rd decimal place by 1

∴ The number correct to 3 decimal places is 8.135

The given number is 0.845

This number up to 2 decimal places is 0.84

The third decimal place is 5

So, we increase the 2nd decimal place by 1

∴ The number correct to 2 decimal places is 0.85

The given number is 1.732

This number up to 1 decimal place is 1.7

The second decimal place is 3 < 5

∴ The number correct to 1 decimal place is 1.7

The given number is 9.638

This number up to 2 decimal places is 9.63

The third decimal place is 8 > 5

So, we increase the 2nd decimal place by 1.

∴ The number correct to 2 decimal places is 9.64

The given number is 0.047

This number up to 2 decimal places is 0.04

The third decimal place is 7 > 5

So, we increase the 2nd decimal place by 1.

∴ The number correct to 2 decimal places is 0.05

The given number is 7.451

Up to hundredths place it is 7.45. The next place is 1 < 5

∴ The required number is 7.45

The given number is 3.157

Up to tenths place it is 3.1. The next place is 5.

So, we increase the tenths place by 1.

∴ The required number is 3.2

The given number is 0.6428

Up to thousandths place it is 0.642. The next place is 8 > 5

So, we increase the thousandths place by 1.

∴ The required number is 0.643

The given number is 0.061

Up to tenths place it is 0.0. The next place is 6 > 5

So, we increase the tenths place by 1.

∴ The required number is 0.1

The given number is 0.136

Up to hundredths place it is 0.13. The next place is 6 > 5

So, we increase the hundredths place by 1.

∴ The required number is 0.14

By actual division, we get:

$$\begin{array}{r} 0.857... \\ 7 \overline{\smash{)} 6.000 } \\ \underline{56} \phantom{.00} \\ 40 \phantom{.0} \\ \underline{35} \phantom{.0} \\ 50 \phantom{} \\ \underline{49} \phantom{} \\ 1 \phantom{} \end{array}$$

The given number up to 2 decimal places is 0.85

The third decimal place is 7 > 5

So, we increase the 2nd decimal place by 1.

∴ $\frac{6}{7}$ correct to 2 decimal places is 0.86

$0.55 = \frac{55}{100}$

= $\frac{11}{20} \quad$ [Dividing both by 5]

Hence, option 2 is the correct option.

$31\frac{3}{8} = 31 + \frac{3}{8}$

Dividing 3 by 8, we get:

$$\begin{array}{r} 0.375 \\ 8 \overline{\smash{)} 3.000 } \\ \underline{24} \phantom{.00} \\ 60 \phantom{.0} \\ \underline{56} \phantom{.0} \\ 40 \phantom{} \\ \underline{40} \phantom{} \\ 0 \phantom{} \end{array}$$

31 + 0.375 = 31.375

Hence, option 3 is the correct option.

Let the required number be x.

5.1 - x = 0.51

x = 5.1 - 0.51

x = 5.10 - 0.51 = 4.59

Hence, option 3 is the correct option.

When multiplying by 100, the decimal point shifts two places to the right.

∴ 92.008 x 100 = 9200.8

Hence, option 4 is the correct option.

Given:

Total runs = 574

Total innings = 8

Average score = Total runs ÷ Total innings

Substituting the values in above, we get:

Average score = 574 ÷ 8

By actual division:

$$\begin{array}{r} 71.75 \\ 8 \overline{\smash{)} 574.00 } \\ \underline{56} \phantom{4.00} \\ 14 \phantom{.00} \\ \underline{8} \phantom{.00} \\ 60 \phantom{.0} \\ \underline{56} \phantom{.0} \\ 40 \phantom{} \\ \underline{40} \phantom{} \\ 0 \phantom{} \end{array}$$

574 ÷ 8 = 71.75

Hence, option 2 is the correct option.

Let x = 0.4555... (i)

Multiplying both sides by 10 (to move the decimal point past the non-repeating digit):

10x = 4.5555... (ii)

Multiplying both sides by 10 (to move the decimal point past the first repeating digit):

100x = 45.5555... (iii)

On subtracting (ii) from (iii), we get:

(100x - 10x) = (45.5555...) - (4.5555...)

90x = 41

$x = \frac{41}{90}$

Hence, option 3 is the correct option.

The given number is 371.6258

Up to two decimal places, it is 371.62

The third decimal digit is 5.

So, we increase the second decimal place by 1.

∴ The required number is 371.63.

Hence, option 2 is the correct option.

(i) For addition or subtraction of decimals, we shall first convert them into like decimals.

(ii) When we multiply a decimal by 1000, we move the decimal three places to the right.

(iii) When we divide a decimal by 100, we move the decimal two places to the left

(iv) When we multiply two decimals, the number of decimal places in the product is equal to the sum of the decimal places in the given decimals.

(v) A decimal in which some of the digits in the decimal part are not repeated while all the rest are repeated, is called a mixed recurring decimal.

(i) False.
Reason — Like decimals have the same number of decimal places, not necessarily the same digits in the decimal parts.

(ii) True.
Reason — The digits to the left of the decimal point represent the whole number part.

(iii) False.
Reason — When dividing decimals, we first make the divisor a whole number. The number of decimal places in the quotient does not depend on the difference in decimal places.

(iv) False.
Reason — A decimal is called terminating if the division ends with a remainder of zero, regardless of what the whole number part is.

(v) False.
Reason — This describes a pure recurring decimal; however, a recurring decimal can also be a mixed recurring decimal where only some digits repeat.

(1) Given:

Cost of one pineapple pastry = ₹25.50

Cost of one patty = ₹12.25

Cost of one doughnut = ₹21.75

Cost of a box of cookies = ₹79.50

Sanya buys:

4 pineapple pastries = 4 x ₹25.50 = ₹102.00

5 patties = 5 x ₹12.25 = ₹61.25

2 doughnuts = 2 x ₹21.75 = ₹43.50

A box of cookies = 1 x ₹79.50 = ₹79.50

Total Bill = ₹(102.00 + 61.25 + 43.50 + 79.50) = ₹286.25

Hence, option 2 is the correct option.

(2) Amount given = ₹500.00

Total Bill = ₹286.25 $\quad$ [From previous step]

Amount received back = (Amount given) - (Total Bill)

Substituting the values in above, we get:

Amount received back = ₹500.00 - ₹286.25 = ₹213.75

Hence, option 4 is the correct option.

(3) Given:

No of pens = 6

Cost of one pen = ₹17.75

Cost of 6 pens = No of pens x Cost of one pen

Cost of 6 pens = 6 x ₹17.75 = ₹106.50

Hence, option 1 is the correct option.

(4) Total amount given = ₹500.00

Money spent on bakery = ₹286.25 $\quad$ [From step 1]

Money spent on pens = ₹106.50 $\quad$ [From step 3]

Final balance returned = ?

Total amount spent = Money spent on bakery + Money spent on pens

Total amount spent = ₹286.25 + ₹106.50 = ₹392.75

Final balance returned = Total amount given - Total amount spent

Substituting the values in above, we get:

Final balance returned = ₹500.00 - ₹392.75 = ₹107.25

Hence, option 4 is the correct option.

(1) Given:

Distance from home to park = 0.42 km

Length of track = 0.37 km

8 rounds of the track = 8 x 0.37 = 2.96 km

Total distance = Distance from home to park + 8 rounds of the track

Substituting the values in above, we get:

Total distance = 0.42 + 2.96 = 3.38 km

Hence, option 2 is the correct option.

(2) Number of rounds = ?

Distance = 4.44 km

Track length = 0.37 km

Number of rounds = Total distance ÷ Track length

Substituting the values in above, we get:

Number of rounds = 4.44 km ÷ 0.37 km = 12

Hence, option 4 is the correct option.

(3) Given:

Distance from home to park = 0.42 km

Length of track = 0.37 km

10 rounds of the track = 10 x 0.37 = 3.70 km

Total distance = Distance from home to park + 10 rounds of the track

Substituting the values in above, we get:

Total distance = 0.42 + 3.70 = 4.12 km

Hence, option 2 is the correct option.

(4) Given:

Distance to park = 0.42 km

Length of track = 0.37 km

8 rounds of track = 8 x 0.37 = 2.96 km

Distance back home = 0.42 km

Total distance = Distance to park + 8 rounds of track + Distance back home

Substituting the values in above, we get:

Total distance = 0.42 km + 2.96 km + 0.42 km = 3.8 km

Hence, option 1 is the correct option.

Assertion (A) is true but Reason (R) is false.

Explanation

When we multiply a decimal by 1000, we shift the decimal point three places to the right.

Example:

2.45 × 1000 = 2450

The Reason is false.

To multiply two decimals, we do not need to convert them into fractions. We multiply the numbers normally and then place the decimal point according to the total number of decimal places.

Hence, option 3 is the correct option.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Explanation

The Assertion is true.

0.2222...... has the digit 2 repeating continuously.

The Reason is also true.

A decimal in which a digit or group of digits repeats continuously is called a recurring decimal.

Since the digit 2 repeats continuously in 0.2222……, it is a recurring decimal.

Hence, option 1 is the correct option.

Assertion (A) is true but Reason (R) is false.

Explanation

In 15.406, the hundredths place is 0. The digit in the thousandths place is 6 > 5, so we increase the hundredths digit by 1 to get 15.41.

The Reason is false.

Nearest hundredths means correct to 2 decimal places, not 3 decimal places.

Hence, option 3 is the correct option.

Given:

46.92 − 89.34 − P = 148.76 − 382.79

Step 1: Simplify the left-hand side (LHS)

46.92 − 89.34 − P

= −42.42 − P $\hspace{2cm}$[∵ 46.92 − 89.34 = −42.42]

Step 2: Simplify the right-hand side (RHS)

148.76 − 382.79

= −234.03

Step 3: Equate LHS and RHS

−42.42 − P = −234.03

−P = −234.03 + 42.42 $\hspace{2cm}$[Transposing −42.42 to RHS]

−P = −191.61

P = 191.61

∴ The value of P is 191.61.

Hence, option 4 is the correct option.

We solve the expression using the BODMAS rule (Brackets, Of, Division, Multiplication, Addition, Subtraction).

Given expression:

1.86 ÷ 0.3 - $\frac{1}{6}$ of (19.3 - 14.5) + 0.3 x 6.8

= 1.86 ÷ 0.3 - $\frac{1}{6}$ of (4.8) + 0.3 x 6.8 $\quad$[Simplifying ()]

= 1.86 ÷ 0.3 - 0.8 + 0.3 x 6.8 $\quad$[Simplifying 'Of']

= 6.2 - 0.8 + 0.3 x 6.8 $\quad$[Solving ÷]

= 6.2 − 0.8 + 2.04 $\quad$[Solving x]

= 8.24 − 0.8 $\quad$[Solving +]

= 7.44 $\quad$[Solving -]

∴ The value of the expression is 7.44.

Hence, option 1 is the correct option.

Step 1: Simplify the numerator

$2\frac{5}{4} - 4\frac{7}{6} + 3\frac{1}{3}$

Converting the mixed fractions into improper fractions:

$$\begin{aligned}2\frac{5}{4} = \frac{2 \times 4 + 5}{4} = \frac{13}{4} \\[1em] 4\frac{7}{6} = \frac{4 \times 6 + 7}{6} = \frac{31}{6} \\[1em] 3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}\end{aligned}$$

So, the numerator becomes:

$\frac{13}{4} - \frac{31}{6} + \frac{10}{3}$

The LCM of 4, 6 and 3 is 12. Taking 12 as the common denominator:

$$\begin{aligned}= \frac{13 \times 3}{12} - \frac{31 \times 2}{12} + \frac{10 \times 4}{12} \\[1em] = \frac{39}{12} - \frac{62}{12} + \frac{40}{12} \\[1em] = \frac{39 - 62 + 40}{12} \\[1em] = \frac{17}{12}\end{aligned}$$

Step 2: Simplify the denominator

0.087 + 0.3717 ÷ 0.9

= 0.087 + $\frac{0.3717}{0.9}$

= 0.087 + $\frac{3.717}{9}$

= 0.087 + 0.413

= 0.5

Step 3: Divide the numerator by the denominator

$$\begin{aligned}\phantom{=}\frac{\frac{17}{12}}{0.5} \\[1em] = \frac{17}{12} \times \frac{1}{0.5} \\[1em] = \frac{17}{12} \times \frac{10}{5} \\[1em] = \frac{17 \times 10}{12 \times 5} \\[1em] = \frac{170}{60} \\[1em] = \frac{17}{6} \\[1em] = 2\frac{5}{6}\end{aligned}$$

∴ The value of the expression is $2\frac{5}{6}$.

Hence, option 1 is the correct option.

Given:

Distance travelled in 1 hour = 13.27 km

Total time = $3\frac{1}{2}$ hours = $\frac{7}{2}$ hours = 3.5 hours

Total distance = Distance travelled in 1 hour × Total time

= 13.27 km × 3.5 hours

Step 1: Multiply the decimals without the decimal point

1327 × 35 = 46445

Step 2: Place the decimal point

Sum of decimal places in given decimals = (2 + 1) = 3

So, the product contains 3 places of decimal.

∴ 13.27 × 3.5 = 46.445

∴ The distance travelled by Swati is 46.445 km.

Hence, option 3 is the correct option.

Given:

2494 ÷ 14.5 = 172

We need to find the value of 24.94 ÷ 1.45.

Step 1: Express 24.94 ÷ 1.45 in terms of the given division

24.94 ÷ 1.45

$$\begin{aligned}= \frac{24.94}{1.45} \\[1em] = \frac{24.94 \times 100}{1.45 \times 100} \\[1em] = \frac{2494}{145}\end{aligned}$$

Step 2: Use the given result

$$\begin{aligned}\frac{2494}{145} \\[1em] = \frac{2494}{14.5 \times 10} \\[1em] = \frac{1}{10} \times \frac{2494}{14.5} \\[1em] = \frac{1}{10} \times 172 \hspace{2cm}[∵ 2494 ÷ 14.5 = 172] \\[1em] = \frac{172}{10}\end{aligned}$$

= 17.2

∴ The value of 24.94 ÷ 1.45 is 17.2.

Hence, option 3 is the correct option.

We know that:

1 hour = 60 minutes

1 minute = 60 seconds

So, 1 hour = 60 × 60 = 3600 seconds

Therefore, 1 second = $\frac{1}{3600}$ hour

Convert $\frac{1}{3600}$ into a decimal

On dividing 1 by 3600, we get:

$\frac{1}{3600}$ = 0.000277....

Rounded off to 5 decimal places, we get 0.00027.

∴ A second is 0.00027 of an hour (approximately).

Hence, option 3 is the correct option.

Given:

Daily insulin requirement (unit) = 0.55 × Total body mass (kilograms)

Total body mass of Khushi = 96 kg

Substituting the value of body mass in the formula:

Daily insulin requirement = 0.55 × 96

Step 1: Multiply the decimal without the decimal point

55 × 96 = 5280

Step 2: Place the decimal point

Number of decimal places in 0.55 = 2

So, the product contains 2 places of decimal.

∴ 0.55 × 96 = 52.80

Rounding 52.80 to the nearest whole number, we get 53.
[∵ first digit to the right of decimal is 8 > 5]

∴ Khushi's daily insulin requirement is 53 units.

Hence, option 1 is the correct option.

Step 1: Find the value of the given expression

2.78 × 0.163

Multiplying the decimals without the decimal point:

278 × 163 = 45314

Sum of decimal places in given decimals = (2 + 3) = 5

So, the product contains 5 places of decimal.

∴ 2.78 × 0.163 = 0.45314

Step 2: Check each option

Checking option 1: 278 × 0.00163

Multiplying the decimal without the decimal point:

278 × 163 = 45314

Number of decimal places in 0.00163 = 5

∴ 278 × 0.00163 = 0.45314

Checking option 2: 27.8 × 1.63

Sum of decimal places = (1 + 2) = 3

∴ 27.8 × 1.63 = 45.314

Checking option 3: 278 × 0.0163

Number of decimal places in 0.0163 = 4

∴ 278 × 0.0163 = 4.5314

Checking option 4: 278 × 16.3

Number of decimal places in 16.3 = 1

∴ 278 × 16.3 = 4531.4

Only option 1 gives the same value as 2.78 × 0.163.

∴ 2.78 × 0.163 = 278 × 0.00163 = 0.45314.

Hence, option 1 is the correct option.

Step 1: Simplify the numerator

0.23 − 0.023

Converting into like decimals:

= 0.230 − 0.023

= 0.207

Step 2: Simplify the denominator

0.0023 ÷ 23

$$\begin{aligned}= \frac{0.0023}{23} \\[1em] = \frac{23}{23 \times 10000} \hspace{2cm}[∵ 0.0023 = \frac{23}{10000}] \\[1em] = \frac{1}{10000} \\[1em] = 0.0001\end{aligned}$$

Step 3: Divide the numerator by the denominator

$$\begin{aligned}\frac{0.207}{0.0001} \\[1em] = \frac{0.207 \times 10000}{0.0001 \times 10000} \\[1em] = \frac{2070}{1} \\[1em] = 2070\end{aligned}$$

∴ The value of the expression is 2070.

Hence, option 3 is the correct option.