Changing Decimals to Fractions

Decimal fraction can be expressed as a fraction with a denominator that is a power of ten. 

Worked Example 7.4.1:

i. Express 0.4 as a fraction
ii. Express 0.37 as a fraction
iii. Express 0.419 as a fraction

Solution

i. Express 0.4 as a fraction

0.4 = \( \frac {4}{10} \)

ii. Express 0.37 as a fraction

0.37 = \( \frac {37}{100} \)

iii. Express 0.419 as a fraction

0.419 = \( \frac {419}{1000} \)

Worked Example 7.4.2:

Express 0.625 as a fraction in its lowest terms. 

Solution 

0.625 = \( \frac {625}{1000} \\ =\frac {625 \div 25}{1000 \div 25} \\ = \frac {25}{40} \)

This is not its lowest term because we can still divide the numerator and denominator by 5

That is, \(\frac {25 \div 5}{40 \div 5}\\ = \frac {5}{8} \)

Worked Example 7.4.3:

Express 0.8 as a fraction in its lowest term 

Solution 

0.8 =  \( \frac {8}{10}\\ = \frac {8 \div 2}{10 \div 2} \\= \frac {4}{5} \)

Hint: The number of decimal places the given decimal number has, determines the power of ten used to divide.