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NumberFoundation and Higher

Calculating with decimals GCSE questions with answers

6 calculating with decimals questions to try, each with the answer and the full working one tap away. Every question here was made and worked out by the Show Working maths engine, not typed in by hand.

This topic is about multiplying and dividing decimals without a calculator. A good method is to work with whole numbers first, then put the decimal point back in the right place.

Quiz yourself: 6 questions

Worked example 1: multiply and divide decimals

Work out 0.5 × 2 without a calculator.

  1. Ignore the decimal points and multiply the whole numbers: 5 × 2 = 10.
  2. Count the digits after the decimal points in the question: 0.5 has 1, and 2 has none. That makes 1 altogether.
  3. So the answer has 1 decimal place: 10 becomes 1.0, which is 1.

Answer 1

01 / Quiz yourselfTry it, then tap to check

Calculating with decimals questions to try

Work each one out on paper first. Then open the answer and compare your working with ours, step by step.

01 / Multiply and divide decimalsBoth tiers

Work out 0.05 × 7 without a calculator.

Show the answer and working
  1. Ignore the decimal points and multiply the whole numbers: 5 × 7 = 35.
  2. Count the digits after the decimal points in the question: 0.05 has 2, and 7 has none. That makes 2 altogether.
  3. So the answer has 2 decimal places: 35 becomes 0.35.

Answer 0.35

02 / Multiply and divide decimalsBoth tiers

Work out 36.4 ÷ 0.7 without a calculator.

Show the answer and working
  1. Make the number you are dividing by into a whole number. Multiply both numbers by 10: 36.4 × 10 = 364, and 0.7 × 10 = 7.
  2. Multiplying both numbers by the same amount does not change the answer: 36.4 ÷ 0.7 = 364 ÷ 7.
  3. Now divide: 364 ÷ 7 = 52.

Answer 52

03 / Multiply and divide decimalsBoth tiers

Work out 3.75 ÷ 1.5 without a calculator.

Show the answer and working
  1. Make the number you are dividing by into a whole number. Multiply both numbers by 10: 3.75 × 10 = 37.5, and 1.5 × 10 = 15.
  2. Multiplying both numbers by the same amount does not change the answer: 3.75 ÷ 1.5 = 37.5 ÷ 15.
  3. Now divide: 37.5 ÷ 15 = 2.5.

Answer 2.5

04 / Multiply and divide decimalsBoth tiers

Work out 3.2 × 0.07 without a calculator.

Show the answer and working
  1. Ignore the decimal points and multiply the whole numbers: 32 × 7 = 224.
  2. Count the digits after the decimal points in the question: 3.2 has 1, and 0.07 has 2. That makes 3 altogether.
  3. So the answer has 3 decimal places: 224 becomes 0.224.

Answer 0.224

05 / Multiply and divide decimalsBoth tiers

Work out 0.09 × 0.8 without a calculator.

Show the answer and working
  1. Ignore the decimal points and multiply the whole numbers: 9 × 8 = 72.
  2. Count the digits after the decimal points in the question: 0.09 has 2, and 0.8 has 1. That makes 3 altogether.
  3. So the answer has 3 decimal places: 72 becomes 0.072.

Answer 0.072

06 / Multiply and divide decimalsBoth tiers

Work out 0.05 × 5 without a calculator.

Show the answer and working
  1. Ignore the decimal points and multiply the whole numbers: 5 × 5 = 25.
  2. Count the digits after the decimal points in the question: 0.05 has 2, and 5 has none. That makes 2 altogether.
  3. So the answer has 2 decimal places: 25 becomes 0.25.

Answer 0.25

02 / What's covered1 kind of question

Calculating with decimals at GCSE and where marks go

  • Multiply and divide decimalsBoth tiers

Worked example 2: multiply and divide decimals

Work out 0.12 × 2 without a calculator.

  1. Ignore the decimal points and multiply the whole numbers: 12 × 2 = 24.
  2. Count the digits after the decimal points in the question: 0.12 has 2, and 2 has none. That makes 2 altogether.
  3. So the answer has 2 decimal places: 24 becomes 0.24.

Answer 0.24

A common mistake

Moving the decimal point in only one number when dividing. To work out 0.216 ÷ 0.06, multiply both numbers by 100 to get 21.6 ÷ 6, which is 3.6.

03 / Practise itiPhone and iPad

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FractionsRoundingStandard formFactors and multiplesNegative numbersFractions, decimals and percentagesPowers and rootsSurdsError intervals and boundsEstimationListing and countingOrder of operationsAll GCSE maths topics
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