Decimals
Place-value numbers using tenths, hundredths, thousandths… after the point.
Key idea
Place-value numbers using tenths, hundredths, thousandths… after the point.
In depth
Decimals extend place value to the right of the point: tenths, hundredths, thousandths, each one tenth of the previous place. They are another way to write fractions with denominators that are powers of 10.
Worked example
0.75 = 7/10 + 5/100 = 75/100 = 3/4.
Formula
Real-world uses
- Money in pounds and pence, metric measurements and lab readings
- Calculator and sensor outputs
Common mistake
Thinking 0.5 and 0.50 differ. Trailing zeros after the point do not change the value.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Decimals?
Place-value numbers using tenths, hundredths, thousandths… after the point. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Decimals?
The key formula is 0.25 = 25/100.
Where is Decimals used in real life?
Real-world examples: Money in pounds and pence, metric measurements and lab readings; Calculator and sensor outputs.
What should I learn before Decimals?
Make sure you are comfortable with Reciprocals, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Decimals?
Thinking 0.5 and 0.50 differ. Trailing zeros after the point do not change the value.
How can I practise Decimals?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Decimals?
Move on to Comparing and Ordering Decimals next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.