Topics
6. Decimals
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AustraliaNSW
Stage 3

6.05 Partition numbers with decimals

Lesson
Practice
Lesson

Are you ready?

We can partition decimals in the same way we partitioned whole numbers. Let's try this problem to review.

Examples

Example 1

We have written a number in the number expander.

A number expander with 3 thousands, 9 hundreds, 8 tens, and 2 units.
a

What is the value of the tens?

Worked Solution
Create a strategy

Use the number in the tens place of the number expander.

Apply the idea

The number says there are 8 tens.

Below is the blocks for 8 tens.

8 columns of squares with 10 squares in each column.

We can see that there are 80 square blocks altogether.

The total value of the tens is 80.

b

What is the value of the hundreds?

Worked Solution
Create a strategy

Use the number in the hundreds place of the number expander.

Apply the idea

The number says there are 9 hundreds.

Below is the blocks for 9 hundreds.

9 squares. Each square has 10 columns of 10 smaller squares.

We can see that there are 900 square blocks altogether.

The total value of the hundreds is 900.

Idea summary

Numbers can be described using any place value such as thousands, hundreds, tens and units.

Break apart decimals using place value

In this video we explore how to write numbers with decimals in expanded form according to their place value representation, we also continue making connections to fractions.

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Examples

Example 2

Fill in the box with the missing number. 0.496 = 0.4 + 0.09+ ⬚

Worked Solution
Create a strategy

Use a place value table to add and subtract the decimals.

Apply the idea

We can add 0.4+0.09 using a place value table.

Ones.TenthsHundredths
0\text{.}40
+ 0\text{.}09
=0\text{.}49

We see that 0.4+0.09=0.49.

To find the number we need to add to 0.49 get 0.496 we can subtract 0.49 from 0.496.

Ones.TenthsHundredthsThousandths
0\text{.}496
- 0\text{.}490
=0\text{.}006

The result is 6 thousandths or 0.006. We can use this value to complete the number sentence.0.496= 0.4+0.09 + 0.006

Idea summary

Number expanders help us to position the number in the correct place value column which can then help us write the number using partitioning.

Outcomes

MA3-7NA

compares, orders and calculates with fractions, decimals and percentages

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