## Subjects

# Fractions and decimals

What is true regarding the number line?

## Fractions and decimals

What’s between the whole numbers on the number line? Right in the middle, between zero and one is one half. We can write this as 1 over 2, a fraction. When we enter 1, divided by, 2 on the calculator, the result is zero point five. So, a fraction, one half, can also be written in decimal form: 0.5.

Exactly in the middle between zero and one half ii one quarter. This fraction too can be written in decimal form: 0.25. Can all fractions be written in decimal form? Lina, Leon and Jenny equally share a bottle with one litre of juice. How big a share of the juice will Leon get?

The juice is shared among three people. Leon gets one out of three equal shares. One third. In fraction form, this is written one over three. If we divide one by three using a calculator, we get 0.333 333 33 and so on.

The threes continue indefinitely even though they can’t be shown on the calculator. We can round off to an approximate value, an approximation. Here we choose two decimal places: 0.33. So: How big a share of the juice does Leon get? We can answer in two ways: Leon gets a third of the juice in the bottle.

This is the answer in fractional form. Or: Leon gets 0.33 litres of juice. This is the answer in decimal form. So, there is a connection between fractional form and decimal form. So yes, all fractions can be written as decimal numbers.

We can also see this connection on the number line. The fraction ‘two fifths’ equals the number ‘zero point four’ in decimal form. The fraction ‘six fifths’ equals the number ’one point two’ in decimal form. Here are a few relationships that are good to commit to memory. One hundredth equals: one over one hundred equals: zero point zero one One tenth equals: one over ten equals: zero point one One half equals: one over two equals: zero point five One quarter equals: one over four equals: zero point two five One fifth equals: one over five equals: zero point two One third equals: one over three approximately equals: zero point three three