Maths
What are decimals?
Quick answer
Decimals are numbers with a decimal point. Digits after the point show tenths, hundredths and so on, so 2.5 means two and five tenths.
In one sentence
A decimal is a way of writing parts of a whole using a decimal point, so 0.5 is the same as one half.
Explained
You already know place value: each column is worth ten times the one to its right. Decimals keep that pattern going past the ones column. The decimal point marks where the whole numbers stop.
| Tens | Ones | . | Tenths | Hundredths |
|---|---|---|---|---|
| 2 | 6 | . | 3 | 8 |
So 26.38 means 2 tens, 6 ones, 3 tenths and 8 hundredths. One tenth is 1 whole split into 10 equal parts. One hundredth is a whole split into 100 parts, which is why a cent or a penny is 0.01 of a dollar or pound.
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ruler
Every decimal is a fraction in disguise. 0.7 = 7/10, 0.07 = 7/100 and 0.25 = 25/100 = ¼. Some fractions turn into decimals that go on forever: ⅓ = 0.333…, with the 3s repeating. See fractions for the other side of this story.
To compare decimals, line up the decimal points and compare column by column from the left. Writing an extra 0 on the end helps and doesn't change the value: 0.5 = 0.50.
To add or subtract, line up the points (just like lining up ones under ones) and work as normal. To multiply by 10, 100 or 1000, the digits move 1, 2 or 3 places to the left.
Examples
- 0.1 = one tenth = 1/10
- 1.5 kg = one and a half kilograms
- 0.6 vs 0.58: write 0.60, so 0.6 is bigger
- 7.45 + 2.8: write 2.8 as 2.80, then 7.45 + 2.80 = 10.25
- 3.07 × 100 = 307
- 45 ÷ 100 = 0.45
Common mistakes
- Thinking a longer decimal is bigger, so 0.125 seems bigger than 0.5. Fix: compare tenths first: 1 tenth against 5 tenths.
- Misreading 0.05 as 0.5. The zero holds the tenths place, so 0.05 is five hundredths.
- Not lining up the points when adding. Fix: write the numbers in columns with the points directly above each other.
- Saying "three point twenty-five" for 3.25. Say "three point two five", because the digits are separate place values.
Quick quiz
Decimals
Check what you know with 5 quick questions.
Question 1 of 5
What is the value of the 4 in 3.47?
Practise it
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Browse maths worksheets and look for decimals and place value pages.
Practise it step by step in a full course: Grade 5 Maths
For grown-ups
Related topics
Place value
Place value means a digit's value depends on its position in a number. In 352, the 3 is worth 300, the 5 is worth 50 and the 2 is worth 2.
Fractions
A fraction is part of a whole that has been split into equal parts. In ¾, the bottom number says how many equal parts and the top says how many you have.
Percentages
A percentage is a number out of 100, written with the sign %. So 25% means 25 out of every 100, which is the same as one quarter.
Rounding
Rounding means replacing a number with a simpler one that is close to it, such as 47 rounded to the nearest ten being 50. It makes numbers easier to work with.
Comparing numbers
Comparing numbers means deciding which is greater, which is less, or if they are equal, and showing it with >, < or =. For example, 52 > 25 because 5 tens is more than 2 tens.
Dividing decimals
To divide by a whole number, divide as usual and put the decimal point straight above. To divide by a decimal, multiply both numbers by 10, 100… until the divisor is whole: 7.2 ÷ 0.6 = 72 ÷ 6 = 12.