Topics
6. Decimals
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Australia
Year 6

6.05 Decimal patterns

Lesson
Practice
Lesson

Are you ready?

In previous lessons we have practiced  writing and recognising decimals  . This skill will help us when we identify patterns involving decimals.

Examples

Example 1

How do we write the number 28.086 in words?

A
Twenty eight units and eighty six thousandths
B
Twenty eight thousand and eighty six
C
Twenty eight units and eight hundred and six thousandths
Worked Solution
Create a strategy

Use the place value table to rewrite the number in words.

Apply the idea
TensUnits.TenthsHundredthsThousandths
28\text{.}086

On the right side of the decimal point, we have 2 tens, and 8 units, which we write as 28 units.

On the left side of the decimal point, we have 0 tenths, 8 hundredths, 6 thousandths, which we write as 86 thousandths.

The number in words is 28 units and 86 thousandths. So the correct answer is A.

Idea summary

One thousandth is written as 0.001 with a\,1 in the thousandths place with 0s as place holders.

Patterns with decimals

This video looks at how to identify the rule and continue a pattern involving decimals.

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Examples

Example 2

Complete the pattern: 4.2, \, 4.0, \, 3.8, \, ⬚, \, ⬚, \, ⬚ .

Worked Solution
Create a strategy

Find how much the numbers are decreasing by each time and subtract that from the last value to complete the pattern.

Apply the idea

To work out how much the numbers are decreasing by each time, you can count up or find the difference between two numbers.

\displaystyle 4.2 - 4.0\displaystyle =\displaystyle 0.2Find the difference

Subtract this result to the last number to complete the pattern.

\displaystyle 3.8 - 0.2\displaystyle =\displaystyle 3.6Subtract 0.2 from 3.8
\displaystyle 3.6 - 0.2\displaystyle =\displaystyle 3.4Subtract 0.2 from 3.6
\displaystyle 3.4 - 0.2\displaystyle =\displaystyle 3.2Subtract 0.2 from 3.4

The complete pattern is 4.2, \, 4.0, \, 3.8, \, 3.6, \, 3.4, \, 3.2.

Idea summary

To continue patterns with decimals, we look for how our numbers are changing. Then we can continue the pattern.

Patterns with decimals across places

This video looks at some pattern concepts where we cross over whole number values, and places.

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Examples

Example 3

Consider the following pattern. 1.8, \, 1.5, \, 1.2, \, ⬚, \, ⬚, \, ⬚

a

What is the pattern?

A
Subtract 0.03
B
Subtract 3
C
Subtract 30
D
Subtract 0.3
Worked Solution
Create a strategy

Find how much the numbers are changing by each time by subtracting two values.

Apply the idea

We can count up or find the difference between two numbers next to each other.

\displaystyle 1.8 - 1.5\displaystyle =\displaystyle 0.3Find the difference

Since 1.5 \lt 1.8 the numbers are decreasing. So we must be subtracting 0.3 each time.

The correct answer is option D.

b

Complete the pattern.

Worked Solution
Create a strategy

Complete the pattern by subtracting 0.3 each time.

Apply the idea

We put the numbers in a place value table, and subtract the digits and regroup where necessary.

Units.Tenths
1.2
-0.3
=0.9

To subtract 0.3 from 1.2, since 2\lt 3 we need to regroup the 1 in the units column to make 12 tenths.

12 tenths - \, 3 tenths =9 tenths.

Units.Tenths
0.9
-0.3
=0.6

To subtract 0.3 from 0.9, we can just subtract the digits down each column.

Units.Tenths
0.6
-0.3
=0.3

To subtract 0.3 from 0.6, we can just subtract the digits down each column.

The complete pattern is: 1.8, \, 1.5, \, 1.2, \, 0.9, \, 0.6, \, 0.3

Idea summary

When continuing a pattern, we need to make sure we remember the place value we are looking at, so we can regroup if necessary.

Outcomes

ACMNA128

Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers

ACMNA133

Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence

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