Topics
6. Decimals
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AustraliaNSW
Stage 3

6.01 Decimals and fractions

Lesson
Practice
Lesson

Are you ready?

Do you know how to convert a fraction into a decimal?

Examples

Example 1

Write the fraction \dfrac{47}{100} as a decimal.

Worked Solution
Create a strategy

Use a place value table.

Apply the idea

\dfrac{47}{100} means 47 hundredths. So we can put this in a place value table:

Ones.TenthsHundredths
0.47
\displaystyle \dfrac{47}{100}\displaystyle =\displaystyle 0.47
Idea summary

If the denominator of a fraction is a power of 10, write the digits in a place value table to convert it into a decimal.

Convert tenths and hundredths

This video looks at decimals in tenths and hundredths and how to convert them between their fraction and decimal form.

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Examples

Example 2

Write the fraction \dfrac{1}{2} as a decimal.

Worked Solution
Create a strategy

Multiply both parts of the fraction by a number that will make the denominator a power of 10.

Apply the idea
\displaystyle \dfrac{1}{2}\displaystyle =\displaystyle \dfrac{1\times5}{2\times5}Multiply both parts by 5
\displaystyle =\displaystyle \dfrac{5}{10}

\dfrac{5}{10} is the same as 5 tenths. To put it in a place value table, put the 5 in the tenths column and use zeros for placeholders:

Unit.Tenths
0\text{.}5

\dfrac{1}{2}=0.5

Idea summary

To convert a fraction to a decimal where the denominator is not a power of 10:

  1. Find a number to multiply or divide the denominator by to make it a power of 10.

  2. Multiply or divide both the numerator and denominator by this number.

  3. Using a place value table or otherwise, write out the number in decimal form.

Convert thousandths

We extend now to thousandths, converting numbers between fractions and decimal form.

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Examples

Example 3

Write the fraction \dfrac{349}{500} as a decimal.

Worked Solution
Create a strategy

Multiply both parts of the fraction by a number that will make the denominator 1000.

Apply the idea
\displaystyle \dfrac{349}{500}\displaystyle =\displaystyle \dfrac{345\times 2}{500\times 2}Multiply both parts by 2
\displaystyle =\displaystyle \dfrac{698}{1000}

\dfrac{698}{1000} is the same as 698 thousandths. To put it in a place value table, put the 6 in the tenths column, 9 in the hundredths column, and 8 in the thousandths column:

Unit.TenthsHundredthsThousandths
0\text{.}698

\dfrac{349}{500}=0.698

Idea summary

To convert fractions to decimals, find an equivalent fraction with tenths, hundredths or thousandths. Then you can use place value to write the decimal.

Outcomes

MA3-7NA

compares, orders and calculates with fractions, decimals and percentages

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