Q1. Write each of the following as decimals:
\begin{array}{l} \text {(i) } \quad \frac{8}{100} \quad \text {(ii) } \quad 20+\frac{9}{10}+\frac{4}{100} \quad \text {(iii) } \quad 23+\frac{2}{10}+\frac{6}{1000} \end{array}\begin{array}{l} \text {Sol. (i) } \quad \frac{8}{100} = 0.08 \\ \\\text {(ii) } \quad 20+\frac{9}{10}+\frac{4}{100} = 20+0.9+0.04 = 20.94 \\ \\\text {(iii) } \quad 23+\frac{2}{10}+\frac{6}{1000} = 23 + 0.2 + 0.006 = 23.206 \end{array}Q2. Convert each of the following into fractions in the lowest form:
(i) 0.04
(ii) 2.34
(iii) 0.342
(iv) 17.38
Sol. \begin{array}{l} \text {(i) } \quad 0.04 = \frac {0.04 \times 100}{100} = \frac {4}{100} = \frac {1}{25} \\ \\\text {(ii) } \quad 2.34 =\frac {2.34 \times 100}{100} = \frac {234}{100} = \frac {117}{50} \\ \\\text {(iii) } \quad 0.342 =\frac {0.342 \times 1000}{1000} = \frac {342}{1000} = \frac {171}{500} \\ \\\text {(iv) } \quad 17.38=\frac {17.38 \times 100}{100} = \frac {1738}{100} = \frac {869}{50} \\ \\ \end{array}Q3. Express the following fractions as decimals:
\begin{array}{l} \text {(i) } \quad \frac{23}{10} \quad \text {(ii) } \quad 25 \frac{1}{8} \quad \text {(iii) } \quad 39 \frac{7}{35} \quad \text {(iv) } \quad 15 \frac{1}{25} \end{array}\begin{array}{l} \text {sol. (i) } \quad \frac{23}{10} = 2.3 \\ \\ \text {(ii) } \quad 25 \frac{1}{8} = 25 + \frac{1}{8} \\ = 25 + \frac{1 \times 125 }{8 \times 125} \\ =25 + \frac{125 }{1000} \\ =25 + 0.125 = 25.125 \\ \\\text {(iii) } \quad 39 \frac{7}{35} = 39 + \frac{7}{35} \\ = 39 + \frac{1}{5} = 39 + \frac{1 \times 20}{5 \times 20 } \\ = 39 + \frac{20}{100 } \\ = 39 + 0.20 = 39.20 \\ \\\text {(iv) } \quad 15 \frac{1}{25} = 15 + \frac{1}{25} \\ = 15 + \frac{1 \times 4}{25 \times 4} \\ = 15 + \frac{ 4}{100} \\ = 15 + 0.04 = 15.04 \\\end{array}Q4. Add the following:
(i) 41.8, 39.24, 5.01 and 62.6
(ii) 18.03, 146.3, 0.829 and 5.324
Sol. (i)\begin{array}{r} 41.8 \\ 39.2 \\ 5.01 \\ +62.6 \\ \hline 148.65 \end{array}(ii) \begin{array}{r} 18.03 \\ 146.3 \\ 0.829 \\ +5.324 \\ \hline 170.483 \end{array}Q5. Find the value of:
(i) 9.756 – 6.28
(ii) 48.1 – 0.37
(iii) 108.032 – 86.8
(iv) 100 – 26.32
Sol. (i) \begin{array}{r} 9.756 \\ -6.28 \\ \hline 3.476 \end{array}(ii)\begin{array}{r} 48.1 \\ -0.37 \\ \hline 47.73 \end{array}(iii) \begin{array}{r} 108.032 \\ -86.8 \\ \hline 21.232 \end{array}(iv) \begin{array}{r} 100 \\ -26.32 \\ \hline 73.68 \end{array}Q6. Take out 3.547 from 7.2
Sol. \begin{array}{r} 7.2 \\ -3.547 \\ \hline 3.653 \end{array}Q7. What is to be added to 36.85 to get 59.41 ?
Sol. Lets assume x be the required number.
Therefore, x + 36.85 = 59.41
$$ \Rightarrow x = 59.41 – 36.85 $$ $$ \Rightarrow x = 22.56 $$ Hence, 22.56 is to be added to 36.85 to get 59.41.
Q8. What is to be subtracted from 17.1 to get 2.051 ?
Sol. Lets assume x be the required number.
$$ \therefore 17.1 – x = 2.051 $$ $$ \Rightarrow x = 17.1 – 2.051 $$ $$ \Rightarrow x = 15.049 $$ Hence, 15.049 is to be subtracted from 17.1 to get 2.051.
Q9. By how much should 34.79 be increased to get 70.15?
Sol. Lets assume x be the required number.
$$ \therefore x + 34.79 = 70.15 $$ $$ \Rightarrow x = 70.15 – 34.79 $$ $$ \Rightarrow x = 35.36 $$ Hence, 35.36 is to added to 34.79 to get 70.15.
Q10. By how much should 59.71 be decreased to get 34.58?
Sol. Lets assume x be the required number.
$$ \therefore 59.71 – x = 34.58 $$ $$ \Rightarrow x = 59.71 – 34.58 $$ $$ \Rightarrow x = 25.13 $$ Hence, 25.13 is to be subtracted from 59.71 to get 34.58.
\begin{array}{l} \text {(i) } \quad \frac{8}{100} \quad \text {(ii) } \quad 20+\frac{9}{10}+\frac{4}{100} \quad \text {(iii) } \quad 23+\frac{2}{10}+\frac{6}{1000} \end{array}\begin{array}{l} \text {Sol. (i) } \quad \frac{8}{100} = 0.08 \\ \\\text {(ii) } \quad 20+\frac{9}{10}+\frac{4}{100} = 20+0.9+0.04 = 20.94 \\ \\\text {(iii) } \quad 23+\frac{2}{10}+\frac{6}{1000} = 23 + 0.2 + 0.006 = 23.206 \end{array}Q2. Convert each of the following into fractions in the lowest form:
(i) 0.04
(ii) 2.34
(iii) 0.342
(iv) 17.38
Sol. \begin{array}{l} \text {(i) } \quad 0.04 = \frac {0.04 \times 100}{100} = \frac {4}{100} = \frac {1}{25} \\ \\\text {(ii) } \quad 2.34 =\frac {2.34 \times 100}{100} = \frac {234}{100} = \frac {117}{50} \\ \\\text {(iii) } \quad 0.342 =\frac {0.342 \times 1000}{1000} = \frac {342}{1000} = \frac {171}{500} \\ \\\text {(iv) } \quad 17.38=\frac {17.38 \times 100}{100} = \frac {1738}{100} = \frac {869}{50} \\ \\ \end{array}Q3. Express the following fractions as decimals:
\begin{array}{l} \text {(i) } \quad \frac{23}{10} \quad \text {(ii) } \quad 25 \frac{1}{8} \quad \text {(iii) } \quad 39 \frac{7}{35} \quad \text {(iv) } \quad 15 \frac{1}{25} \end{array}\begin{array}{l} \text {sol. (i) } \quad \frac{23}{10} = 2.3 \\ \\ \text {(ii) } \quad 25 \frac{1}{8} = 25 + \frac{1}{8} \\ = 25 + \frac{1 \times 125 }{8 \times 125} \\ =25 + \frac{125 }{1000} \\ =25 + 0.125 = 25.125 \\ \\\text {(iii) } \quad 39 \frac{7}{35} = 39 + \frac{7}{35} \\ = 39 + \frac{1}{5} = 39 + \frac{1 \times 20}{5 \times 20 } \\ = 39 + \frac{20}{100 } \\ = 39 + 0.20 = 39.20 \\ \\\text {(iv) } \quad 15 \frac{1}{25} = 15 + \frac{1}{25} \\ = 15 + \frac{1 \times 4}{25 \times 4} \\ = 15 + \frac{ 4}{100} \\ = 15 + 0.04 = 15.04 \\\end{array}Q4. Add the following:
(i) 41.8, 39.24, 5.01 and 62.6
(ii) 18.03, 146.3, 0.829 and 5.324
Sol. (i)\begin{array}{r} 41.8 \\ 39.2 \\ 5.01 \\ +62.6 \\ \hline 148.65 \end{array}(ii) \begin{array}{r} 18.03 \\ 146.3 \\ 0.829 \\ +5.324 \\ \hline 170.483 \end{array}Q5. Find the value of:
(i) 9.756 – 6.28
(ii) 48.1 – 0.37
(iii) 108.032 – 86.8
(iv) 100 – 26.32
Sol. (i) \begin{array}{r} 9.756 \\ -6.28 \\ \hline 3.476 \end{array}(ii)\begin{array}{r} 48.1 \\ -0.37 \\ \hline 47.73 \end{array}(iii) \begin{array}{r} 108.032 \\ -86.8 \\ \hline 21.232 \end{array}(iv) \begin{array}{r} 100 \\ -26.32 \\ \hline 73.68 \end{array}Q6. Take out 3.547 from 7.2
Sol. \begin{array}{r} 7.2 \\ -3.547 \\ \hline 3.653 \end{array}Q7. What is to be added to 36.85 to get 59.41 ?
Sol. Lets assume x be the required number.
Therefore, x + 36.85 = 59.41
$$ \Rightarrow x = 59.41 – 36.85 $$ $$ \Rightarrow x = 22.56 $$ Hence, 22.56 is to be added to 36.85 to get 59.41.
Q8. What is to be subtracted from 17.1 to get 2.051 ?
Sol. Lets assume x be the required number.
$$ \therefore 17.1 – x = 2.051 $$ $$ \Rightarrow x = 17.1 – 2.051 $$ $$ \Rightarrow x = 15.049 $$ Hence, 15.049 is to be subtracted from 17.1 to get 2.051.
Q9. By how much should 34.79 be increased to get 70.15?
Sol. Lets assume x be the required number.
$$ \therefore x + 34.79 = 70.15 $$ $$ \Rightarrow x = 70.15 – 34.79 $$ $$ \Rightarrow x = 35.36 $$ Hence, 35.36 is to added to 34.79 to get 70.15.
Q10. By how much should 59.71 be decreased to get 34.58?
Sol. Lets assume x be the required number.
$$ \therefore 59.71 – x = 34.58 $$ $$ \Rightarrow x = 59.71 – 34.58 $$ $$ \Rightarrow x = 25.13 $$ Hence, 25.13 is to be subtracted from 59.71 to get 34.58.