Decimal Fractions — Exercise 5(C)

Convert each of the following decimals into a fraction with lowest terms:

(i) 0.8

(ii) 0.06

(iii) 0.45

(iv) 0.64

(v) 5.4

(vi) 6.25

(vii) 8.125

(viii) 3.475

Answer

(i) Writing the decimal 0.8 as a fraction,

0.8 = $\dfrac{8}{10}=\dfrac{4}{5}$

Therefore, the required fraction is $\dfrac{4}{5}$ .

(ii) Writing the decimal 0.06 as a fraction,

0.06 = $\dfrac{6}{100}=\dfrac{3}{50}$

Therefore, the required fraction is $\dfrac{3}{50}$ .

(iii) Writing the decimal 0.45 as a fraction,

0.45 = $\dfrac{45}{100}=\dfrac{9}{20}$

Therefore, the required fraction is $\dfrac{9}{20}$ .

(iv) Writing the decimal 0.64 as a fraction,

0.64 = $\dfrac{64}{100}=\dfrac{16}{25}$

Therefore, the required fraction is $\dfrac{16}{25}$ .

(v) Writing the decimal 5.4 as a fraction,

5.4 = $\dfrac{54}{10}=\dfrac{27}{5}=5\dfrac{2}{5}$

Therefore, the required fraction is $5\dfrac{2}{5}$ .

(vi) Writing the decimal 6.25 as a fraction,

6.25 = $\dfrac{625}{100}=\dfrac{25}{4}=6\dfrac{1}{4}$

Therefore, the required fraction is $6\dfrac{1}{4}$ .

(vii) Writing the decimal 8.125 as a fraction,

8.125 = $\dfrac{8125}{1000}=\dfrac{65}{8}=8\dfrac{1}{8}$

Therefore, the required fraction is $8\dfrac{1}{8}$ .

(viii) Writing the decimal 3.475 as a fraction,

3.475 = $\dfrac{3475}{1000}=\dfrac{139}{40}=3\dfrac{19}{40}$

Therefore, the required fraction is $3\dfrac{19}{40}$ .

Convert each of the following fractions into decimals:

(i) $\dfrac{9}{10}$

(ii) $\dfrac{23}{10}$

(iii) $\dfrac{427}{10}$

(iv) $\dfrac{37}{100}$

(v) $\dfrac{107}{100}$

(vi) $\dfrac{1423}{100}$

(vii) $\dfrac{123}{1000}$

(viii) $\dfrac{2045}{1000}$

Answer

(i) Converting the fraction $\dfrac{9}{10}$ into a decimal,

$\dfrac{9}{10}=0.9$

Therefore, the decimal form is 0.9 .

(ii) Converting the fraction $\dfrac{23}{10}$ into a decimal,

$\dfrac{23}{10}=2\dfrac{3}{10}=2+\dfrac{3}{10}=2+0.3=2.3$

Therefore, the decimal form is 2.3 .

(iii) Converting the fraction $\dfrac{427}{10}$ into a decimal,

$\dfrac{427}{10}=42\dfrac{7}{10}=42+\dfrac{7}{10}=42+0.7=42.7$

Therefore, the decimal form is 42.7 .

(iv) Converting the fraction $\dfrac{37}{100}$ into a decimal,

$\dfrac{37}{100}=0.37$

Therefore, the decimal form is 0.37.

(v) Converting the fraction $\dfrac{107}{100}$ into a decimal,

$\dfrac{107}{100}=1\dfrac{7}{100}=1+\dfrac{7}{100}=1+0.07=1.07$

Therefore, the decimal form is 1.07 .

(vi) Converting the fraction $\dfrac{1423}{100}$ into a decimal,

$\dfrac{1423}{100}=14\dfrac{23}{100}=14+\dfrac{23}{100}=14+0.23=14.23$

Therefore, the decimal form is 14.23.

(vii) Converting the fraction $\dfrac{123}{1000}$ into a decimal,

$\dfrac{123}{1000}=0.123$

Therefore, the decimal form is 0.123 .

(viii) Converting the fraction $\dfrac{2045}{1000}$ into a decimal,

$\dfrac{2045}{1000}=2\dfrac{45}{1000}=2+\dfrac{45}{1000}=2+0.045=2.045$

Therefore, the decimal form is 2.045 .

Convert each of the following fractions into decimals:

(i) $\dfrac{3}{20}$

(ii) $\dfrac{7}{25}$

(iii) $\dfrac{9}{50}$

(iv) $\dfrac{1}{4}$

(v) $\dfrac{16}{125}$

(vi) $\dfrac{231}{250}$

(vii) $\dfrac{17}{500}$

(viii) $\dfrac{8}{250}$

Answer

(i) Converting the fraction $\dfrac{3}{20}$ into a decimal,

$\dfrac{3}{20}=\dfrac{3\times5}{20\times5}=\dfrac{15}{100}=0.15$

Therefore, the decimal form is 0.15.

(ii) Converting the fraction $\dfrac{7}{25}$ into a decimal,

$\dfrac{7}{25}=\dfrac{7\times4}{25\times4}=\dfrac{28}{100}=0.28$

Therefore, the decimal form is 0.28.

(iii) Converting the fraction $\dfrac{9}{50}$ into a decimal,

$\dfrac{9}{50}=\dfrac{9\times2}{50\times2}=\dfrac{18}{100}=0.18$

Therefore, the decimal form is 0.18.

(iv) Converting the fraction $\dfrac{1}{4}$ into a decimal,

$\dfrac{1}{4}=\dfrac{1\times25}{4\times25}=\dfrac{25}{100}=0.25$

Therefore, the decimal form is 0.25.

(v) Converting the fraction $\dfrac{16}{125}$ into a decimal,

$\dfrac{16}{125}=\dfrac{16\times8}{125\times8}=\dfrac{128}{1000}=0.128$

Therefore, the decimal form is 0.128.

(vi) Converting the fraction $\dfrac{231}{250}$ into a decimal,

$\dfrac{231}{250}=\dfrac{231\times4}{250\times4}=\dfrac{924}{1000}=0.924$

Therefore, the decimal form is 0.924.

(vii) Converting the fraction $\dfrac{17}{500}$ into a decimal,

$\dfrac{17}{500}=\dfrac{17\times2}{500\times2}=\dfrac{34}{1000}=0.034$

Therefore, the decimal form is 0.034.

(viii) Converting the fraction $\dfrac{8}{250}$ into a decimal,

$\dfrac{8}{250}=\dfrac{8\times4}{250\times4}=\dfrac{32}{1000}=0.032$

Therefore, the decimal form is 0.032.

Convert each of the following fractions into decimals:

(i) $5\dfrac{3}{4}$

(ii) $3\dfrac{1}{4}$

(iii) $6\dfrac{1}{5}$

(iv) $12\dfrac{4}{5}$

(v) $7\dfrac{3}{8}$

(vi) $2\dfrac{4}{25}$

(vii) $3\dfrac{7}{20}$

(viii) $4\dfrac{11}{20}$

Answer

(i) $5\dfrac{3}{4} = \dfrac{5 \times 4 + 3}{4} = \dfrac{23}{4}$

By actual division, we have:

$\begin{array}{l} \phantom{4)}{\space \phantom{2} 5.75} \\ 4\overline{\smash{\big)}\space 23.00} \\ \phantom{4)}\phantom{)}\underline{20} \\ \phantom{4)\space 2}30 \\ \phantom{4)\space 2}\underline{28} \\ \phantom{4)\space 28}20 \\ \phantom{4)\space 28}\underline{20} \\ \phantom{4)\space 28}\times \end{array}$

$\therefore 5\dfrac{3}{4} = \dfrac{23}{4} = 5.75$

Therefore, the decimal form is 5.75.

(ii) $3\dfrac{1}{4}=\dfrac{3\times4 + 1}{4}=\dfrac{13}{4}$

By actual division, we have:

$\begin{array}{l} \phantom{4)}{\space \phantom{2} 3.25} \\ 4\overline{\smash{\big)}\space 13.00} \\ \phantom{4)}\phantom{)}\underline{12} \\ \phantom{4)\space 2}10 \\ \phantom{4)\space 22}\underline{8} \\ \phantom{4)\space 28}20 \\ \phantom{4)\space 28}\underline{20} \\ \phantom{4)\space 28}\times \end{array}$

Therefore, the decimal form is 3.25.

(iii) $6\dfrac{1}{5}=\dfrac{6\times5 + 1}{5}=\dfrac{31}{5}$

$\begin{array}{l} \phantom{5)}{\space \phantom{2} 6.2} \\ 5\overline{\smash{\big)}\space 31.0} \\ \phantom{5)}\phantom{)}\underline{30} \\ \phantom{5)\space 2.}10 \\ \phantom{5)\space 2.}\underline{10} \\ \phantom{5)\space 28}\times \end{array}$

Therefore, the decimal form is 6.2.

(iv) $12\dfrac{4}{5}=\dfrac{12 \times 5 + 4}{5}=\dfrac{64}{5}$

$\begin{array}{l} \phantom{5)}{\space 12.8} \\ 5\overline{\smash{\big)}\space 64.0} \\ \phantom{5)}\phantom{)}\underline{5} \\ \phantom{5)\space .}14 \\ \phantom{5)\space .}\underline{10} \\ \phantom{5)\space 21}40 \\ \phantom{5)\space 55}\underline{40} \\ \phantom{5)\space 28.}\times \end{array}$

Therefore, the decimal form is 12.8.

(v) $7\dfrac{3}{8}=\dfrac{7 \times 8 + 3}{8}=\dfrac{59}{8}$

$\begin{array}{l} \phantom{8)}{\space \phantom{)} 7.375} \\ 8\overline{\smash{\big)}\space 59.000} \\ \phantom{8)}\phantom{)}\underline{56} \\ \phantom{8)\space )}030 \\ \phantom{8)\space )}\underline{\phantom{2}24} \\ \phantom{8)\space 22)}60 \\ \phantom{8)\space 55}\underline{\phantom{)}56} \\ \phantom{8)\space 222)}40 \\ \phantom{8)\space 55}\underline{\phantom{2)}40} \\ \phantom{8)\space 2831}\times \end{array}$

Therefore, the decimal form is 7.375.

(vi) $2\dfrac{4}{25}=\dfrac{25 \times 2 + 4 }{25}=\dfrac{54}{25}$

$\begin{array}{l} \phantom{25)}{\space \phantom{)} 2.16} \\ 25\overline{\smash{\big)}\space 54.00} \\ \phantom{25)}\phantom{)}\underline{50} \\ \phantom{25)\space ))}40 \\ \phantom{25)\space ))}\underline{25} \\ \phantom{25)\space ))}150 \\ \phantom{25)\space ))}\underline{150} \\ \phantom{25)\space 28)}\times \end{array}$

Therefore, the decimal form is 2.16.

(vii) $3\dfrac{7}{20}=\dfrac{3 \times 20 + 7}{20}=\dfrac{67}{20}$

$\begin{array}{l} \phantom{20)}{\space \phantom{)} 3.35} \\ 20\overline{\smash{\big)}\space 67.00} \\ \phantom{20)}\phantom{)}\underline{60} \\ \phantom{20)\space ))}70 \\ \phantom{20)\space ))}\underline{60} \\ \phantom{20)\space ))}100 \\ \phantom{20)\space ))}\underline{100} \\ \phantom{20)\space 28)}\times \end{array}$

Therefore, the decimal form is 3.35.

(viii) $4\dfrac{11}{20}=\dfrac{4 \times 20 + 11}{20}=\dfrac{91}{20}$

$\begin{array}{l} \phantom{20)}{\space \phantom{)} 4.55} \\ 20\overline{\smash{\big)}\space 91.00} \\ \phantom{20)}\phantom{)}\underline{80} \\ \phantom{20)\space )}110 \\ \phantom{20)\space )}\underline{100} \\ \phantom{20)\space )))}100 \\ \phantom{20)\space )))}\underline{100} \\ \phantom{20)\space 28))}\times \end{array}$

Therefore, the decimal form is 4.55.