Each place is worth ten times the place to its right. To multiply or divide decimals, work with whole numbers first, then put the decimal point back by counting places or by estimating.
Ignore the decimal points and work out the whole-number answer: 0.3×0.04→3×4=12.
Count the decimal places in the question (1+2=3) and give the answer that many: 0.012.
Check with an estimate: 0.3×0.04 is about a third of 0.04, so 0.012 makes sense.
Watch out For positive numbers, multiplying by a number between 0 and 1 makes the answer smaller, and dividing by one makes it bigger.
See it worked
Worked exampleNon-calculator·4 marks
Answer each part without a calculator.
(a) Work out 0.3×0.4
(b) Work out 4.8÷0.6
(c) Write down the largest of 0.407,0.47 and 0.4.
(a) 3×4=12. There are two decimal places in the question, so there are two in the answer: 0.12.
(b) Multiply both numbers by 10: 48÷6=8.
(c) Compare with the same number of decimal places: 0.407,0.470,0.400. The largest is 0.470.
Answer (a) 0.12; (b) 8; (c) 0.47
Your turn
Question 1Calculator allowed·2 marks
A customer pays with a £20 note for three notebooks costing £2.65 each. Work out the change.
Question 2Non-calculator·2 marks
Work out 3.6 ÷ 0.24.
Question 3Non-calculator·4 marks
A straight fence is 14.4 m long. It is made from panels 1.8 m wide, placed end to end. There is a post at each end of the fence and one post between each pair of neighbouring panels. Each panel costs £23.75 and each post costs £6.40.
Work out the total cost of the panels and posts for the fence.
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