Why decimals are fractions

Quick answer

Decimals are just another way to write fractions. The numbers after the decimal point show tenths, hundredths, and smaller parts – exactly like fractions with denominators of 10, 100, 1000, and so on.

Learning outcome

By the end of this page, you will understand that decimals are simply fractions written in a different way, and you can convert between them easily.

• You can identify the place value of digits in decimals (tenths, hundredths).
• You can write decimals as fractions with denominators of 10 or 100.
• You can write fractions as decimals when the denominator is 10 or 100.
• You can use real-life examples like money or measurements to understand decimals and fractions.

Why this matters

Decimals are everywhere in daily life – from money (like £2.50), to measuring things (like 1.75 metres), to recipes (like 0.5 litres of milk). Understanding that decimals are just fractions helps you work with numbers more confidently. It also helps you solve problems more easily, especially when you need to compare or add numbers.

How it works

When we write a decimal number, each digit has a place value. The first digit after the decimal point is the tenths place, and the second is the hundredths place. For example:

1. The number 0.6 means 6 tenths, which is the same as the fraction 6/10.
2. The number 0.25 means 2 tenths and 5 hundredths, which is the same as the fraction 25/100.
3. When we have a whole number and a decimal, like 3.4, it means 3 whole ones and 4 tenths, or 3 4/10.

Examples you can see

Let’s look at some examples using things you can see and touch:

Imagine you have a chocolate bar cut into 10 equal pieces. If you eat 3 pieces, you have eaten 3 tenths of the bar. That’s the same as 0.3 of the bar. If you eat 7 pieces, you have eaten 7 tenths, or 0.7 of the bar.

Try it as a mini adventure

Adventure: The Decimal Bakery

You are the head baker at a magical bakery where all prices are written in decimals. You need to make sure you know how to read the prices and match them to the right amounts of ingredients.

1. First stop: The sugar shelf shows a price tag of £0.40. You know that 40 pence is the same as 40/100 of a pound. What fraction is this?
2. Second stop: The flour bag is £0.75. You need to know how many hundredths this is. What fraction is this?
3. Third stop: The eggs are £1.30. This is 1 pound and 30 pence. What fraction is this?
4. Final challenge: You have a recipe that calls for 0.5 kg of butter. How many hundredths is this?

By the end of your adventure, you should be able to match each decimal to its correct fraction!

Common mistakes

• Mistake: Thinking that 0.7 is the same as 7/100. Why it happens: Confusing the place values. Fix: Remember that the first digit after the decimal is tenths, so 0.7 = 7/10.
• Mistake: Writing 0.3 as 3/100 instead of 3/10. Why it happens: Not understanding decimal place value. Fix: Count the digits after the decimal point. One digit = tenths.
• Mistake: Mixing up 0.25 and 25/100. Why it happens: Thinking the decimal point doesn’t matter. Fix: Remember 0.25 = 25/100, because 25 hundredths = 25/100.

Parent and carer guide

As a parent or carer, you can help your child by:

• Using real-life examples like money or measurements to show how decimals and fractions are the same.
• Practising together by converting decimals to fractions and vice versa.
• Encouraging your child to say out loud what each digit means in a decimal number.
• Playing simple games like “decimal bingo” or using fraction cards with decimal numbers.
• Not worrying if your child makes mistakes – they’re part of learning!

Practice questions

1. Write 0.6 as a fraction.
2. Convert 0.25 to a fraction.
3. Write 1.3 as a mixed number fraction.
4. Convert 0.8 to a fraction.
5. Write 2.07 as a mixed number fraction.

Answers:

1. 0.6 = 6/10
2. 0.25 = 25/100
3. 1.3 = 1 3/10
4. 0.8 = 8/10
5. 2.07 = 2 7/100

FAQ

Why are decimals and fractions the same?

They are both ways to show parts of a whole. Decimals just use a different way of writing the same idea – using place values like tenths and hundredths.

How do I know if a decimal is tenths or hundredths?

The first digit after the decimal point is tenths. The second is hundredths. So 0.3 = 3 tenths, and 0.35 = 3 tenths and 5 hundredths.

Can all decimals be written as fractions?

Yes! Every decimal can be written as a fraction with a denominator of 10, 100, 1000, and so on.

How do I write 0.12 as a fraction?

0.12 = 12/100, because there are two digits after the decimal point, so it’s hundredths.

Is 0.5 the same as 5/10?

Yes! 0.5 means 5 tenths, which is exactly the same as 5/10.