6.01 Tenths and hundredths

Lesson

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

VCMNA159

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