Topics
6. Decimals
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Australia
Year 6

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

ACMNA131

Make connections between equivalent fractions, decimals and percentages

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