# 6.01 Tenths and hundredths

Lesson

## Ideas

We have previously worked with the  fraction one tenth  or \dfrac{1}{10}. Represent this fraction on the following number line.

### Examples

#### Example 1

Plot \dfrac{1}{10} on the number line.

Worked Solution
Create a strategy

The space between 0 and 1 on the number line has been divided into 10 equal spaces. Use the fraction bar model to count.

Apply the idea

\dfrac{1}{10} is equal to 1 lot of \dfrac{1}{10}. So we need to move 1 space from 0.

Idea summary

We plotting fractions on a number line the denominator tells us how many equal parts to split the number line into.

## Create decimals in tenths and hundredths

This video shows you how to write a number as both a fraction and decimal for numbers that are both tenths and hundredths.

### Examples

#### Example 2

Look at the diagram.

a

What fraction of the total squares are shaded?

Worked Solution
Create a strategy

Write the fraction as \dfrac{\text{number of shaded parts}}{\text{total number of parts}}.

Apply the idea

There are 26 shaded squares out of 100 squares. So the fraction is: \dfrac{26}{100}

b

Write the fraction as a decimal.

Worked Solution
Create a strategy

Use a place value table to convert it to a decimal.

Apply the idea

The fraction is 26 hundredths. To put it in a place value table, we put the last digit, 6 in the hundredths column and put 2 in the column to the left of hundredths. Then we use zeros for place holders:

\dfrac{26}{100}=0.26

Idea summary

We can use a place value table to convert a fraction to a decimal.

## Tenths

When we looked at place value, we looked at how numbers can be written in a place value table so we can write and understand the value of a number. We started with the units column, then went up to tens, hundreds, thousands and so on. This video shows how we can use the place value columns for numbers less than 1 whole.

### Examples

#### Example 3

Write the decimal 5.3 as an improper fraction.

Worked Solution
Create a strategy

Put each digit in a place value table then add their values.

Apply the idea

To put the decimal in a place value table, place the 5 in the units column and the 3 in the tenths column:

5 units is equal to 5, and 3 tenths is equal to \dfrac{3}{10}. Now we can add these values:

Idea summary

To convert a decimal into a fraction, we can use a place value table to work out the value of each digit. Then we can add the values together.

## Hundredths

Continuing on from tenths this video now looks at how we can extend to hundredths.

### Examples

#### Example 4

Write the following fraction as a decimal: \dfrac{9}{100}

Worked Solution
Create a strategy

Use a place value table to convert it to a decimal.

Apply the idea

The fraction is 9 hundredths. To put it in a place value table, put the 9 in the hundredths column and use zeros for place holders:

\dfrac{9}{100}=0.09

Idea summary

10 tenths make 1 whole.

100 hundredths make 1 whole.

### Outcomes

#### MA2-7NA

represents, models and compares commonly used fractions and decimals