Decimals
A decimal is a way of writing a number that is not a whole number, using a decimal point to separate whole units from tenths, hundredths and smaller parts. 11+ papers test place value, ordering, rounding and the four operations with decimals, all without a calculator.
Before you start
Make sure you're comfortable with these topics first:
Method
- Line up decimal points when adding or subtracting, padding shorter numbers with zeros so every column matches.
- When multiplying decimals, multiply the digits as whole numbers first, then count the total number of decimal places in both numbers to place the decimal point in the answer.
- When dividing a decimal by 10, 100 or 1000, move the decimal point left by 1, 2 or 3 places; when multiplying, move it right instead.
- To multiply or divide two decimals, it can help to convert one to a whole number first, for example by multiplying both numbers by 10, and adjust the answer afterwards.
- Convert between decimals, fractions and percentages by remembering that the digits after the decimal point show tenths, hundredths and thousandths as a fraction over 10, 100 or 1000.
- Check your answer's size makes sense: multiplying by a number less than 1 should give a smaller result, not a larger one.
Worked example
Work out 3.6 x 0.5, without using a calculator.
- Ignore the decimal points for now and multiply the digits as whole numbers: 36 x 5 = 180.
- Count the total number of decimal places in the original numbers: 3.6 has 1 decimal place and 0.5 has 1 decimal place, giving 2 in total.
- Place the decimal point in 180 so that there are 2 digits after it: 1.80.
- Simplify by removing the unnecessary trailing zero: 1.8.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Work out 5.4 - 2.75, showing your working.
Amir buys 3.5 kg of potatoes at 0.80 pounds per kilogram and a bag of onions costing 1.20 pounds. (a) Calculate the cost of the potatoes. (b) Calculate the total cost of the potatoes and onions. (c) Calculate his change from a 5 pound note.
A recipe needs 0.65 kg of flour, 0.3 kg of butter and 150 g of sugar. Priya has a 1 kg bag of flour, a 500 g pack of butter and a 200 g bag of sugar. (a) Calculate the total mass of flour, butter and sugar needed for the recipe, giving your answer in kilograms. (b) State, with a reason, whether Priya has enough of all three ingredients.
Free printable worksheet
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