 # 6.02 Read and write numbers with decimals

Lesson

## Ideas

In the past, we have learned how to  recognise place value of digits in whole numbers  to help us compare numbers. Let's practice.

### Examples

#### Example 1

What is the place value of 8 in 486\,327?

A
Tens of thousands
B
Thousands
C
Hundreds of thousands
Worked Solution
Create a strategy

Use a place value table.

Apply the idea

If we put the number in a place value table we get the following:

We can see that 8 is in the ten thousands column. So the correct answer is A.

Idea summary

We can use a place value table to identify the place value of the digits in a number.

## Tenths and hundredths

This video looks at the representations of numbers as words and symbols for tenths and hundredths.

### Examples

#### Example 2

Write the number "sixty six hundredths" as a decimal.

Worked Solution
Create a strategy

We can use a place value table to help us write the decimal.

Apply the idea

To put it in a place value table, put the 6 in the hundredths column first as it is the last digit of the number, 6 in the tenths column, and use zeros for place holders:

66 \text{ hundredths}=0.66

Idea summary

We can use a place value table to convert a number in words into a decimal.

## Thousandths

This video shows us how to read and write thousandths.

### Examples

#### Example 3

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

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.

## Smaller than thousandths

This video shows us how to read and write numbers that are smaller than thousandths.

### Examples

#### Example 4

Choose the numeral representation of the following:

Three thousand, nine hundred and ninety one tens of thousandths

A
0.3991
B
0.399\,11
C
0.3791
Worked Solution
Create a strategy

We can use a place value table to help us write the decimal.

Apply the idea

To put it in a place value table, put the 1 in the ten thousands column first as it is the last digit of the number. Then we put the remaining digits in the columns to the left: 9 in the thousands column, 9 in the hundredths column, 3 in the tenths column, and use zeros for place holders:

3991 tens of thousandths is equal to 0.3991. So the correct answer is A.

Idea summary

The pattern in the naming of the place value column for whole numbers has the same pattern when we go the other way for decimals. Instead of tens, hundreds, thousands, ten thousands; we have tenths, hundredths, thousandths and ten thousandths.