Decimals
Ordering decimals, converting between fractions and decimals, and performing calculations with decimal numbers.
What is Decimals?
Decimals are another way of representing parts of a whole, using the base-10 system. The digits after the decimal point represent tenths, hundredths, thousandths and so on.
In the 11+ exam, you may need to order decimals, add and subtract them, multiply and divide by powers of 10, and convert between decimals and fractions or percentages.
Step-by-Step Method
Know decimal place values
The first digit after the decimal point is tenths, the second is hundredths, the third is thousandths.
For ordering, add trailing zeros
Make all decimals the same length by adding zeros at the end. Then compare digit by digit from left to right.
Line up decimal points for addition and subtraction
Write the numbers with the decimal points aligned. Fill empty places with zeros.
For multiplying by 10, 100, 1000 move the decimal point
Move the decimal point right by the number of zeros. For dividing, move it left.
Convert fractions to decimals by dividing
Divide the numerator by the denominator. For example, 3/8 = 3 divided by 8 = 0.375.
Worked Examples
Put in order from smallest to largest: 0.7, 0.65, 0.705
Working
- Add trailing zeros: 0.700, 0.650, 0.705.
- Compare: 650 < 700 < 705.
- Order: 0.65, 0.7, 0.705.
Convert 5/8 to a decimal.
Working
- Divide 5 by 8.
- 5.000 / 8 = 0.625.
- So 5/8 = 0.625.
3.47 x 100 = ?
Working
- Move the decimal point 2 places to the right.
- 3.47 becomes 347.
Common Mistakes
Thinking 0.9 is less than 0.15 because 9 < 15.
Compare tenths first: 0.9 has 9 tenths, 0.15 has 1 tenth. So 0.9 > 0.15.
Moving the decimal point the wrong way when multiplying or dividing.
Multiplying by 10/100/1000 moves the point RIGHT. Dividing moves it LEFT.
Not lining up decimal points when adding, leading to the wrong answer.
Always write the decimal points directly above each other and fill gaps with zeros.
Top Tips
- Learn the common fraction-to-decimal conversions: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 1/8 = 0.125.
- When ordering decimals, adding trailing zeros removes all confusion.
- Check your decimal point position by estimating first. If 3.2 x 4 should be about 12, your answer of 128 means the point is wrong.
- To convert a decimal to a fraction, count the decimal places: 0.35 = 35/100 = 7/20.
Ready to practise?
Put these techniques into action with our free practice papers.
Practise Maths Questions