Conversion of Fractions to Decimals

Changing Fractions to Decimals: 

To express a fraction as a decimal, make an equivalent fraction with a denominator that is a power of ten. 

Worked Example 7.5.1:

Express\(\frac {3}{5} \)as a decimal. 

Solution:

\( \frac {3}{5} = \frac {3}{5} \: \times \: \frac {10}{10}\\ = \frac {30}{50} \\= \frac {6}{10}\\ = \scriptsize 0.6 \)

Note: 5 in 30 gives 6 and 5 in 50 gives 10. 

Worked Example 7.5.2:

Express \( \frac {6}{25}\)as a decimal 

Solution:

To make the denominator in power of 10 we multiply the numerator and denominator it by 4 to get 100. We are looking for the number that will multiply 25 to get 100.

Note: We can also obtain the number by dividing 100 by 25

⇒ \( \frac {100}{25} \scriptsize = 4 \)

Hence  

⇒ \( \frac {6}{25} \\= \frac {6 \: \times \: 4}{25 \: \times \: 4} \\= \frac {24}{100} \\ = \scriptsize 0.24\)

Worked Example 7.5.3:

Express\( \frac {5}{8}\)as a decimal. 

Solution 

\( \frac {5}{8} \\ = \frac {5 \: \times \: 1000}{8 \: \times \: 1000} \\= \frac {5000}{8000} \\ = \frac {625}{1000} \\ \scriptsize = 0.625\)

Ans = 0.625

Hint: To make 8000 to the power of 10 we divide it by 8. i.e 8000 ÷ 8 = 1000 and 5000 ÷ 8 = 625. It is easier to divide with the power of ten as the denominator which in this case is 1000.