Content description

Investigating terminating and recurring decimals (ACMNA184)

Elaboration

• recognising terminating, recurring and non-terminating decimals and choosing their appropriate representations

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

Writing decimals as fractions and mixed numbers

To write 0.005 as a decimal, note that there are no tenths, no hundredths and five thousandths, and thus we know \(0.005 = \dfrac{5}{1000} = \dfrac{1}{200}\)

To write 2.36 as a mixed number, we write \(2.36 = 2\dfrac{36}{100} = 2\dfrac{9}{25}\)

Writing fractions and mixed numbers as decimals

If we have a fraction in which the denominator is a power of 10, it is easy to convert 
it to a decimal. For example,

\(2\dfrac{34}{100} = 2.34\)

This can also be done as:

\(2\dfrac{34}{100} = 2 + \dfrac{30}{100} + \dfrac{4}{100} = 2.34\)

All positive numbers have a decimal representation.

Some fractions have a denominator that is a factor of a power of 10. The following example shows how to write such a fraction as a decimal.

Example 1

Convert \(\dfrac{3}{5}\) and \(\dfrac{3}{125}\) to decimals by finding an equivalent fraction with a denominator that is a power of 10.

Solution

\(\dfrac{3}{5}=\dfrac{3 ×2}{5×2}=\dfrac{6}{10}=0.6\hspace{4em}\dfrac{3}{125}=\dfrac{3×8}{125×8}=\dfrac{24}{1000}=0.024\)