1. Teacher Notes
This PowerPoint presentation has been designed to support teachers to deliver a series of lessons on decimal numbers.
It specifically addresses the Australian Curriculum content descriptors for Mathematics: Number and Algebra – Fractions and decimals.
For additional teaching resources, browse the Fractions, Decimals and Percentages collection on the Teach Starter website. Some specific resources to compliment this PowerPoint include:
Representing Tenths Worksheet
Representing Hundredths Worksheet

2. Symbols
I do: my turn to talk. This is the explanation section of our lesson where you are required to listen. We do: this is where we discuss or work on the concepts together. You do: your turn to be involved. You may be working in a group or on an activity individually.

3. Introducing Decimal Numbers

4. Decimal Numbers in Everyday Life
She is 7.5 years old.
He is 8.5 years old.
She is 1.23 m tall.
He is 1.28 m tall.
She has $7.65 in her piggy bank.
He has $3.40 in his piggy bank.
She lives 2.25 km from school.
This is Joanna.
This is Joshua.
He lives 1.75 km from school.
What do the numbers on this slide have in common?

5. Decimal Numbers in Everyday Life
Decimal numbers are all around us. They are so common in our everyday lives that we may not even realise when we are using them! Some decimal numbers include:
amounts of money
temperatures
distances
masses
times.
Can you think of any others?

6. Why Do We Need Decimal Numbers?
Sometimes, whole numbers are just not precise enough to meet our needs. For example, what might happen if…
… a grocer wanted to charge between $2 and $3 for her bananas?
… the temperature for the day fell between 37°C and 38°C?
… a carpenter wanted timber between 1 metre and 2 metres?
… a sprinter finished a race between 8 seconds and 9 seconds?
… a baby weighed between 3 kilograms and 4 kilograms?
Can you think of any other examples like this?

7. What is a Decimal Number?
A decimal number is another way of writing a number which contains a fraction.
Decimal numbers may be less than or greater than 0.
The decimal point is used to separate the whole numbers from the fractions. It is always placed between the units column and the tenths column.
whole number
fraction
(six tenths)
23.6
decimal point

8. Place Value in Decimal Numbers
When writing decimal numbers, each digit holds a place. This place represents the value of that digit within the number.
If there are any whole numbers in the decimal, these belong on the left-hand side of the decimal place. Any fractions, or parts of a whole, belong on the right-hand side of the decimal place.
Hundreds
Tens
Units
Tenths
Hundredths
whole numbers
fractions

9. Place Value in Decimal Numbers - Tenths and Hundredths
The first column on the right-hand side of the decimal point is the tenths column. The tenths column is ten times smaller than the units column.
The second column on the right-hand side of the decimal point is the hundredths column. The hundredths column is ten times smaller than the tenths column.
6.28
units
tenths
hundredths

10. Writing Fractions as Decimals - Tenths
This square represents one whole.
The whole has been divided into ten equal parts.
Another way of saying this is that the square has been divided into ten tenths.
= 1 whole

11. Writing Fractions as Decimals - Tenths
This coloured bar represents one tenth of the whole square.
As a fraction, this is written as
As a decimal, this is written as 0.1.

12. Writing Tenths as Decimals – Example
What fraction does the coloured section represent? How is this written as a decimal?
The coloured section represents four tenths of the whole.
As a fraction, this is written as
As a decimal, this is written as 0.4.

13. Writing Tenths as Decimals - Review
Fill in the missing information in each of the questions below.
a) three tenths = = 0.
b) six tenths = = 0.
c) nine tenths = = 0.
d) four tenths = = 0.
e) five tenths = = 0.
f) one tenth = = 0.
g) eight tenths = = 0.
h) two tenths = = 0.

14. Writing Tenths as Decimals - Answers
Fill in the missing information in each of the questions below.
a) three tenths = = 0.3
b) six tenths = = 0.6
c) nine tenths = = 0.9
d) four tenths = = 0.4
e) five tenths = = 0.5
f) one tenth = = 0.1
g) eight tenths = = 0.8
h) two tenths = = 0.2

15. Writing Fractions as Decimals - Hundredths
This square represents one whole.
The whole has been divided into one hundred equal parts.
Another way of saying this is that the square has been divided into one hundred hundredths.
= 1 whole

16. Writing Fractions as Decimals - Hundredths
These coloured squares represent forty-three hundredths of the whole square.
As a fraction, this is written as
As a decimal, this is written as 0.43.

17. Writing Hundredths as Decimals – Example
What fraction does the coloured section represent? How is this written as a decimal?
The coloured section represents seventy-eight hundredths of the whole.
As a fraction, this is written as
As a decimal, this is written as 0.78.

18. Writing Hundredths as Decimals - Review
Fill in the missing information in each of the questions below.
a) eighteen hundredths = = 0.
b) sixty-one hundredths = = 0.
c) forty-nine hundredths = = 0.
d) two hundredths = = 0.
e) twelve hundredths = = 0.
f) thirty-one hundredths = = 0.
g) sixty-nine hundredths = = 0.
h) seven hundredths = = 0.

19. Writing Hundredths as Decimals - Answers
Fill in the missing information in each of the questions below.
a) eighteen hundredths = = 0.18
b) sixty-one hundredths = = 0.61
c) forty-nine hundredths = = 0.49
d) two hundredths = = 0.02
e) twelve hundredths = = 0.12
f) thirty-one hundredths = = 0.31
g) sixty-nine hundredths = = 0.69
h) seven hundredths = = 0.07