 # 6.04 Compare decimals

Lesson

Let's  practice writing decimals from their written form  .

### Exploration

Use the applet below to convert a number of tenths into a fraction.

When writing a number of tenths as a fraction we should write the number as the numerator and use a denominator of 10.

### Examples

#### Example 1

Let's look at the number 50 tenths.

a

Write this number as a fraction.

Worked Solution
Create a strategy

Write the number above a denominator of 10.

Apply the idea

50 \text{ tenths } = \dfrac{50}{10}

b

Now write the same number as a decimal.

Worked Solution
Create a strategy

Use the fraction found in part (a) and put it in a place value table.

Apply the idea

Since we are dealing with a tenths number, we will be placing the last digit of our numerator, 0, into the tenths column and the first digit, 5, in the column to the left.

So 50 tenths in decimal form is 5.0.

Idea summary

When writing a number of tenths as a fraction we should write the number as the numerator and use a denominator of 10.

## Compare decimals up to hundredths

Anytime we are comparing numbers, the important thing we need to consider is the value of the numbers we are comparing. Just like 6 hundreds are worth more than 6 tens, we need to consider the value of the digits in a number with decimals. In this video we look at how we can visualise the value of our numbers, helping to identify bigger or smaller numbers.

### Examples

#### Example 2

Choose the smaller decimal

A
8.9
B
8.4
Worked Solution
Create a strategy

Use a place value table and compare the numbers.

Apply the idea

Comparing from the units column, both numbers have the same value so we move to the next place value which is the tenths column.

In the tenths column, 4 is smaller than 9.

So the correct answer is 8.4 or option B.

Idea summary

We can compare decimals using a place value table, starting from the highest place value.

## Compare decimals using equivalent decimals

When we compare decimals, it also helps to remember that some numbers may look different, but are in fact equivalent. While 0.3 and 0.30 may look different, they have the same value. Using equivalent fractions can help, since fractions are another way to express parts of a whole. In this video, we show how we can compare decimals, while keeping in mind that we may be able to express a number more than one way, just like we did above, with 3 tenths and 30 hundredths.

### Examples

#### Example 3

Choose the larger decimal.

A
3.3
B
3.38
Worked Solution
Create a strategy

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

Apply the idea

We can put 0 at the end of 3.3 so that the two decimals have the same number of decimal places, making them easier to compare.

As we can see in the table, both numbers have the same value in the units and tenths column, so we move to the hundredths column.

In the hundredths colums, 8 is larger than 0.

So the larger decimal is option B or 3.38.

Idea summary

When comparing decimals with a different number of decimal places, we can use zeros as place holders in a place value table.

## Make a statement true

In this video we make a statement true, by thinking about whether one side is equal to, greater than, or less than the other side.

### Examples

#### Example 4

Write the greater than \gt or less than \lt symbol in the box to make this number sentence true:

9.1 \,⬚\, 9.57

Worked Solution
Create a strategy

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

Apply the idea

As we can see in the table, both numbers have the same value in the units column, so we move to the tenths column.

In the tenths colums, 1 \lt 5 which means that 9.1 is less than 9.57.

So the correct statement is 9.1<9.57.

Idea summary

\gt means 'greater than'

\lt means 'less than'.

### Outcomes

#### VCMNA159

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