By rounding each number to 1 significant figure, estimate (7.83 × 29.6) ÷ 0.412.
- Round: 7.83 becomes 8, 29.6 becomes 30, 0.412 becomes 0.4.
- Top: 8 × 30 = 240.
- Divide: 240 ÷ 0.4 = 2400 ÷ 4 = 600.
Answer: 600
Estimation
Maths · Number. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
Rounding gives a simpler value that is close to the exact one. You may be asked to round to a number of decimal places, to a number of significant figures, or to the nearest 10, 100 and so on.
The first significant figure is the first digit that is not zero. Zeros in front of it only hold the place and are not counted. Look at the next digit after the one you keep: 5 or more rounds up, 4 or less leaves it unchanged.
To estimate a calculation, round every number to 1 significant figure and then work it out. In a real problem, give an answer that makes sense: no more accurate than the data, and a whole number when you are counting things.
Rules to remember
- Significant figures are counted from the first non-zero digit: 0.004 07 has 3 significant figures.
- Next digit 5 or more: round up. Next digit 4 or less: leave the digit as it is.
- Keep the size of the number: 48 651 to 2 significant figures is 49 000, not 49.
- Keep a final zero if it is significant: 2.596 to 3 significant figures is 2.60.
- Estimating: round each number to 1 significant figure, then calculate.
- Dividing by a number less than 1 makes the answer bigger: 240 ÷ 0.4 = 600.
- Round up when a whole number of containers or vehicles must hold everything.
Common mistake
Counting the leading zeros as significant figures. In 0.030 496 the first significant figure is the 3, so 3 significant figures gives 0.0305.
Worked example
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