Topics
6. Percentages
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Australia
Year 5

6.02 Percentages as decimals

Lesson
Practice

Are you ready?

Remembering how to  read and write decimals  will help us in this lesson. Let's try a practice problem to review.

Examples

Example 1

Write the number "sixty six hundredths" as a decimal.

Worked Solution
Create a strategy

Use a place value table.

Apply the idea

Since there are 66 hundredths, we put the second 6 in the hundredths column and the first 6 in the column to the left.

Units.TenthsHundredths
0.66

Sixty six hundredths is equal to 0.66.

Idea summary

A place value table for decimals:

HundredsTensUnits.TenthsHundredths
\text{}

We can use 0 as a placeholder for any empty place value columns.

Convert decimals to percentages

This video looks at how to write decimals in percentage form.

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Examples

Example 2

Write 0.23 as a percentage.

Worked Solution
Create a strategy

To write a decimal as a percentage multiply by 100\%.

Apply the idea

To multiply a decimal by 100, we can write it in a place value table and then move the digits 2 places to the left:

TensUnits.TenthsHundredths
\text{Original decimal}0.23
\times 10023

0.23=23\%

Idea summary

We can convert any decimal into a percentage by multiplying the decimal by 100, which is equivalent to increasing the place value of each digit by two places, and attaching a \% symbol.

Convert percentages to decimals

This video looks at how to write percentages in decimal form.

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Examples

Example 3

Write 90\% as a decimal.

Worked Solution
Create a strategy

To write a percentage as a decimal divide by 100.

Apply the idea

To divide a decimal by 100, we can write it in a place value table and then move the digits 2 places to the right:

TensUnits.TenthsHundredths
\text{Original percentage}90.
\div 1000.90

0.90 = 0.9 so our final answer is: 90\%=0.9

Idea summary
  • A percentage is an amount out of 100. For example 42\% is 42 out of 100.
  • Decimals can also be written in hundredths, such as 0.42.
  • 0.42 is the same as 42\%.

Outcomes

AC9M5N04

recognise that 100% represents the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to their decimal and fraction equivalents

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