Rounding, estimating and bounds Cambridge IGCSE Mathematics (9–1) revision
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In plain words
No measurement is exact. "8 cm to the nearest centimetre" could be anything from 7.5 up to just under 8.5. Rounding tidies numbers up, estimating checks whether an answer is sensible, and bounds tell you how far off a rounded number might be.
Three things to know
- Decimal places count digits after the point. Significant figures start counting at the first digit that isn't zero: 0.004729 is 0.0047 to 2 significant figures.
- To estimate, round every number to 1 significant figure and then calculate.
- Bounds: a number rounded to the nearest unit could be half a unit either way. 8 cm to the nearest cm has lower bound 7.5 cm and upper bound 8.5 cm. For the biggest possible a − b or a ÷ b, use the upper bound of a and the lower bound of b.
Worked example
A rectangle measures 6 cm by 4 cm, each to the nearest centimetre. Find the upper bound of its area.
- Upper bounds of the sides: 6.5 cm and 4.5 cm.
- Largest possible area = 6.5 × 4.5.
- = 29.25 cm².
Tips and tricks
- Leading zeros are not significant. Zeros between other digits, and zeros after them past the decimal point, are.
- To make a division as big as possible: biggest top, smallest bottom.
It lands in your notebook with its questions as flashcards.
Rounding, estimating and bounds: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is 3.846 correct to 2 decimal places?
The third decimal digit is 6, so round up.
What is 0.004729 correct to 2 significant figures?
Start counting at the 4.
A length is 25 cm to the nearest centimetre. What is its lower bound?
Half a centimetre below.
Estimate 19.8 × 5.1.
20 × 5.
A number is 3.4 correct to 1 decimal place. What is its upper bound?
Half of 0.1 above.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
4 questions, 9 marks. Write your answers on paper, then check them.
Rounding, estimating and bounds
Cambridge IGCSE Mathematics (9–1) 0980 · 9 marks · papermunch.org
Name ______________________________ Date ______________
Write 0.04567 correct to 2 significant figures, and 4728 correct to 2 significant figures.[2]
Show answerHide answer
0.046 and 4700.
By rounding each number to 1 significant figure, estimate (48.7 × 2.1) ÷ 0.49.[2]
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200. (50 × 2) ÷ 0.5.
A mass is 62 kg, correct to the nearest kilogram. Write down its lower and upper bounds.[2]
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61.5 kg and 62.5 kg.
a = 10 and b = 4, each to the nearest whole number. Find the upper bound of a ÷ b.[3]
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3. 10.5 ÷ 3.5.
Answers: Rounding, estimating and bounds
- 1. 0.046 and 4700.
- 2. 200. (50 × 2) ÷ 0.5.
- 3. 61.5 kg and 62.5 kg.
- 4. 3. 10.5 ÷ 3.5.