## Working in tenths

When we work with number lines, we need to look at the end points and the ticks in between. This tells us the value of each tick, so we know what to count by.

For the number line below, we can see that the endpoints are $0$0 and $1$1 and there are $10$10 spaces, so each tick represents $\frac{1}{10}$110, or $0.1$0.1.

When we need to plot or work out decimals and fractions with tenths on one number line, we can think about how we could say the value. For example $0.2$0.2 is the same as $\frac{2}{10}$210, which we can say as, "$2$2 tenths." Have a look at some examples in Video 1.

Remember!

Decimals and fractions are just different ways to express the same number.

## Zooming in

We can also zoom in, with different end points and look at number lines with hundredths and thousandths. If we break $\frac{1}{10}$110 into $10$10 pieces, we have $\frac{10}{100}$10100.

What happens if we split $\frac{1}{100}$1100 into $10$10 pieces? Have a look at Video 2 to see what happens when we zoom in to smaller pieces.

## Let's plot!

Now we are ready to plot fractions and decimals to the hundredths and thousandths. It's really important to look at the end points to help us work out the value of the ticks in between. Remember:

- If the end points on our number line are $1$1 tenth apart and broken into $10$10 equal pieces, each tick is worth $1$1 hundredth.
- If the end points on our number line are $1$1 hundredth apart and broken into $10$10 equal pieces, each tick is worth $1$1 thousandth.

Let's plot some to work through it more closely.

## What are these numbers?

Are you ready to see if you can work out the value of these numbers on the number line? They could be hundredths or thousandths, so see how you go!

#### Worked examples

##### Question 1

Plot both the decimal $0.1$0.1 and the fraction $\frac{5}{10}$510 on the number line below.

##### Question 2

What number is shown on the following number line?

Write the number as a decimal.

Write the number as a fraction.

##### Question 3

Plot both the decimal $3.864$3.864 and the fraction $\frac{3866}{1000}$38661000 on the number line.