 # Tenths, 100ths and Decimals

Lesson ## Representing decimals

Decimal numbers can be represented using:

• words
• numbers
• symbols
• pictures

Take a look back to review tenths and hundredths as equivalent fractions.

In this chapter we will be looking at representing decimals with words, numbers and symbols. Take a look at this video to learn more about decimals.

We can change the decimal notation we use depending on the problem.

It is important for us to understand all representations to know which to use and how to change them if needed.

We can use place value columns to help us understand decimals.

## Starting with words

#### Example 1

Represent fifty six tenths as a fraction and as a decimal number.

If we put this in a place value column it looks like this:

Units . Tenths Hundredths
. 56

Tenths as a fraction has a denominator of 10, so it is $\frac{56}{10}$5610

With place value we can only have one digit in each column. As our number system is based on ten, we know that 50 tenths is the same as 5 units so my place value column looks like this:

Units . Tenths Hundredths
5 . 6

As a number this is 5.6

Try this question for yourself.

##### Question 1:

Write the following as a decimal:

$85$85 tenths

## Starting with symbols

#### Example 2

Represent $\frac{285}{100}$285100 as a number and in words.

If we put this in a place value column it looks like this:

Units . Tenths Hundredths
.   285

In words, this is two hundred and eighty five hundredths.

In place value we can only have one digit in each column. As our number system is based on ten the 280 hundredths is the same as 28 tenths, so I can adjust the place value column to look like this:

Units . Tenths Hundredths
. 28 5

Again, because our number system is based on ten, the 20 tenths is the same as 2 units. So now our place value columns look like this:

Units . Tenths Hundredths
2 . 8 5

As a decimal number this is 2.85

Try this question for yourself.

##### Question 2:

Write the fraction $\frac{107}{100}$107100 as a decimal.

## Starting with numbers

#### Example 3

Write 3.49 in words and as a fraction.

Using our place value columns the number looks like this:

Units . Tenths Hundredths
3 . 4 9

Again, because our number system is based on ten, the 3 units is the same as 30 tenths. So I can adjust the digits to look like this:

Units . Tenths Hundredths
. 34 9

Now, the 34 tenths is the same as 340 hundredths, so I can adjust the digits to look like this:

Units . Tenths Hundredths
.   349

In words, this is three hundred and forty nine hundredths.

As a fraction hundredths have a denominator of 100, so it is $\frac{349}{100}$349100

Try this question for yourself.

##### Question 3:

Write the decimal $6.05$6.05 as an improper fraction.