Decimals
Decimals are numbers with a decimal point. They are used for money, measurements, percentages and many GCSE calculation questions.
In 4.372:
4 is the units digit
3 is the tenths digit
7 is the hundredths digit
2 is the thousandths digit
Decimal place value
Place value helps you understand the size of each digit in a decimal. Digits after the decimal point get ten times smaller each step to the right.
Example 1: Identify decimal place value
In the number 12.548, what is the value of the digit 4?
The 4 is in the hundredths column.
4 hundredths = 0.04
Ordering decimals
To order decimals, line up the decimal points and compare digits from left to right.
Example 2: Order decimals
Put these numbers in ascending order:
0.7, 0.67, 0.706, 0.076
Add zeros to help compare:
0.700, 0.670, 0.706, 0.076
Ascending order: 0.076, 0.67, 0.7, 0.706
Rounding decimals
When rounding, look at the digit immediately after the place you are rounding to.
Example 3: Round to 1 decimal place
Round 6.47 to 1 decimal place.
The tenths digit is 4. The next digit is 7.
Since 7 is 5 or more, round up.
6.47 ≈ 6.5
Example 4: Round to 2 decimal places
Round 3.14159 to 2 decimal places.
The second decimal place is 4. The next digit is 1.
Since 1 is less than 5, keep the 4 the same.
3.14159 ≈ 3.14
Adding and subtracting decimals
Line up decimal points before adding or subtracting decimals.
Example 5: Add decimals
Calculate 3.75 + 12.6.
Write 12.6 as 12.60 to line up the decimal places.
3.75 + 12.60 = 16.35
Example 6: Subtract decimals
Calculate 9.2 - 4.83.
Write 9.2 as 9.20.
9.20 - 4.83 = 4.37
Multiplying decimals
Multiply as whole numbers first, then place the decimal point carefully.
Example 7: Multiply decimals
Calculate 0.6 × 0.4.
First calculate 6 × 4 = 24.
There are two decimal places in total in the question.
0.6 × 0.4 = 0.24
Converting decimals to percentages
To convert a decimal to a percentage, multiply by 100.
Example 8: Decimal to percentage
Convert 0.37 to a percentage.
0.37 × 100 = 37%
Converting decimals to fractions
Use place value to write decimals as fractions.
Example 9: Decimal to fraction
Write 0.45 as a fraction.
0.45 means 45 hundredths:
0.45 = 45/100 = 9/20
A common mistake is comparing decimals by length. For example, 0.706 is bigger than 0.7, but 0.076 is smaller. Line up decimal points and compare digits carefully.
In non-calculator questions, estimate first. This helps you spot decimal place errors in your final answer.
Video explanation
A short Worthing Maths Tutor video explanation for decimals can be embedded here later to improve student engagement and time on page.
Practice questions
- What is the value of the digit 6 in 8.364?
- Put in ascending order: 0.41, 0.405, 0.5, 0.045.
- Round 7.86 to 1 decimal place.
- Calculate 5.7 + 3.84.
- Convert 0.62 to a percentage.
Answers
- 6 hundredths, or 0.06
- 0.045, 0.405, 0.41, 0.5
- 7.9
- 9.54
- 62%
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