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decimals

Decimal equivalents of tenths

Connect tenths fractions directly to decimal notation.

Quick answer

Decimal equivalents of tenths means converting fractions like 1/10, 2/10, 3/10, and so on into decimal numbers like 0.1, 0.2, 0.3, and so on.

Learning outcome

By the end of this page, you will be able to convert fractions with a denominator of 10 into decimal numbers and understand how tenths work in both fraction and decimal form. Success signs:
  • You can write 1/10 as 0.1 and 3/10 as 0.3
  • You can match tenths fractions to their decimal equivalents
  • You can explain how 10 tenths make one whole
  • You can use tenths in real-life situations like money or measuring

Why this matters

Understanding decimal equivalents of tenths helps you in many real-life situations. When you shop and see prices like £1.50, that 50p is five tenths of a pound. When you measure ingredients for a recipe, you might use 0.3 of a cup of sugar. Knowing how tenths work in decimals helps you make better sense of money, measurements, and even scores in games or sports. This is the first step toward understanding hundredths and more complex decimals later on.

How it works

Decimal numbers are a way to show parts of a whole. When we have 10 equal parts, each part is one-tenth. If we take some of those parts, we can show that as a fraction or as a decimal. Let’s start with a simple example:
  • 1 whole is divided into 10 equal pieces
  • Each piece is 1/10 or 0.1
  • If we take 3 pieces, we have 3/10 or 0.3
Think of a pizza cut into 10 equal slices. If you eat 1 slice, you've eaten 1/10 of the pizza. If you eat 4 slices, you've eaten 4/10 of the pizza. In decimal form, that's 0.1, 0.2, 0.3, 0.4.

Examples you can see

Here are some examples of tenths as decimals:
Fraction Decimal
1/10 0.1
2/10 0.2
3/10 0.3
4/10 0.4
5/10 0.5
6/10 0.6
7/10 0.7
8/10 0.8
9/10 0.9
10/10 1.0
Let’s imagine you are making a bar chart for a school project. Each bar is 10 cm long, and you colour in 1 cm for each tenth. If you colour in 3 cm, you have 3/10 or 0.3 of the bar. If you colour in 7 cm, you have 7/10 or 0.7 of the bar. Another example: You have a ribbon that is 1 metre long. You cut it into 10 equal pieces. Each piece is 1/10 of a metre, which is 0.1 metres. If you use 4 pieces, you have used 4/10 or 0.4 metres.

Try it as a mini adventure

Adventure: The Decimal Garden You are a gardener who needs to plant flowers in rows. Each row is 10 cm long. You have a special measuring tool that shows tenths.
  • 1st time: You plant 1 flower in the first 1 cm of the row. That's 1/10 or 0.1 of the row.
  • 2nd time: You plant 2 flowers in the next 2 cm. That's 2/10 or 0.2 of the row.
  • 3rd time: You plant 5 flowers in 5 cm. That's 5/10 or 0.5 of the row.
  • 4th time: You plant 10 flowers in all 10 cm. That's 10/10 or 1.0 of the row.
Can you write the decimal for each step? What happens when you plant 10 flowers in a row?

Common mistakes

  • Mistake: Thinking 3/10 = 0.30
    Why it happens: Confusing the decimal place value
    Fix: Remember that 3/10 is just 3 tenths, so it's 0.3, not 0.30
  • Mistake: Writing 1/10 as 1.0
    Why it happens: Not understanding that 10 parts make one whole
    Fix: 1/10 is one of ten equal parts, so it's 0.1
  • Mistake: Mixing up 0.7 and 7/10
    Why it happens: Not seeing that they are the same thing
    Fix: 0.7 is the same as 7/10 because both show 7 parts out of 10

Parent and carer guide

Parents and carers can help by:
  • Using everyday items like coins, rulers, or measuring cups to show tenths
  • Practising with a number line that goes from 0 to 1, divided into 10 equal parts
  • Playing a game where you say a fraction and the child says the decimal, or vice versa
  • Looking for tenths in real life: prices ending in .10, .20, .30, etc.
  • Using visual aids like fraction circles or strips to show how 10 tenths make one whole
At home, you can ask your child:
  • What is 4/10 in decimal form?
  • How many tenths make one whole?
  • Can you find 0.6 on a ruler?
Remember: It's okay if they get it wrong at first. Learning decimals is a process, and it's normal to make mistakes.

Practice questions

  1. What is 1/10 as a decimal?
  2. What is 5/10 as a decimal?
  3. What is 8/10 as a decimal?
  4. What is 10/10 as a decimal?
  5. What is 0.3 as a fraction?
  6. What is 0.7 as a fraction?
  7. What is 0.9 as a fraction?
  8. What is 0.1 as a fraction?
Answers:
  1. 0.1
  2. 0.5
  3. 0.8
  4. 1.0
  5. 3/10
  6. 7/10
  7. 9/10
  8. 1/10

FAQ

What does "tenths" mean in maths?

In maths, "tenths" means one of ten equal parts. When you divide something into 10 equal pieces, each piece is one-tenth.

How do I convert tenths fractions to decimals?

To convert a fraction like 3/10 to a decimal, just write the numerator (3) in the tenths place after the decimal point. So 3/10 = 0.3.

Why is 1/10 the same as 0.1?

Because 1/10 means 1 part out of 10 equal parts. In decimal form, that's 0.1, with the 1 in the tenths place.

Can I write 0.5 as a fraction?

Yes! 0.5 is the same as 5/10, because it has 5 in the tenths place.

What comes after 0.9 in decimals?

After 0.9 comes 1.0, which means one whole. 1.0 is the same as 10/10.