Topics
6. Decimals
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AustraliaVIC
Level 4

6.05 Order decimals

Lesson
Practice
Lesson

Are you ready?

We have used place value to help us  order whole numbers  before. Let's try a practice problem to help us remember.

Examples

Example 1

Order these numbers from largest to smallest.

a

73,\ 33,\ 37

Worked Solution
Create a strategy

Use a place value table and compare the numbers.

Apply the idea
TensUnits
73
33
37

Comparing from the tens column, 7 is largest value which means 73 is the largest number.

33 and 37 have the same tens value so we move to the units.

7 is larger than 3. This means that 37 \gt 33.

So the correct order is: 73,\ 37,\ 33

b

671,\ 167,\ 617

Worked Solution
Create a strategy

Use a place value table and compare the numbers.

Apply the idea
HundredsTensUnits
671
167
617

Comparing from the hundreds column, 1 is the smallest value which means that the smallest number is 167.

671 and 617 have the same value in the hundreds column so we move to the tens.

7 is larger than 1. This means that 671\gt 617.

So the correct order is: 671,\ 617,\ 167

Idea summary

We can use a place value table to compare whole numbers.

Order decimals with tenths

This video looks at ways to compare decimals with both units and tenths.

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Examples

Example 2

Choose the smaller decimal

A
0.6
B
0.4
Worked Solution
Create a strategy

Use a place value table and compare the numbers.

Apply the idea
Units.Tenths
0.6
0.4

Both numbers have the same value in the units column.

Comparing the tenths, we find that 4 is smaller than 6.

So the smaller decimal is 0.4 or option B.

Idea summary

We can use a place value table to compare decimals with tenths.

Order decimals with hundredths

In this video we will work through some examples, using a couple of different ways to order the list of numbers. Importantly, remember that it is the place value of the numbers we are comparing.

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Examples

Example 3

Which of these sets are arranged from smallest to largest?

A
0.92,\ 0.47,\ 0.35
B
0.35,\ 0.47,\ 0.92
C
0.47,\ 0.35, 0.92
Worked Solution
Create a strategy

Use a place value table and compare the numbers.

Apply the idea
Units.TenthsHundredths
0.35
0.47
0.92

All decimals have the same units value.

Comparing from the tenths column, we see that 3 is the smallest value, followed by 4 and the largest is 9.

So the arrangement of the numbers should be: 0.35,\ 0.47,\ 0.92 The correct answer is option B.

Idea summary

We can use a place value table to compare decimals with hundredths.

Rename tenths as hundredths

Sometimes it can be useful when we need to compare a mixture of numbers with tenths and hundredths to renaming the tenths to hundredths. We see an example of this in the next video.

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Examples

Example 4

Arrange the following decimals from smallest to largest: 0.7,\ 0.09,\ 0.61

Worked Solution
Create a strategy

Use a place value table and compare the numbers. Use 0 as a placeholder.

Apply the idea
Units.TenthsHundredths
0.70
0.09
0.61

All decimals have the same units value.

Comparing from the tenths column, we see that 0 is the smallest value, followed by 6 and the largest is 7.

So the arrangement of the numbers from smallest to largest is: 0.09,\ 0.61,\ 0.7

Idea summary

When our numbers have units and tenths, we need to always compare the place value furthest to the left because it has the largest place value. We cannot only look at how long each number is.

Outcomes

VCMNA159

Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation

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