Decimal places
- To round to 2 decimal places, look at the third decimal place: 5 or more rounds up, 4 or less rounds down. 3.476 → 3.48.
- Keep the zero if it's needed: 7.95 to 1 decimal place is 8.0.
Significant figures
- The first significant figure is the first non-zero digit. 45 672 to 2 s.f. is 46 000; 0.003 482 to 2 s.f. is 0.0035.
- Zeros between non-zero digits are significant: 0.0506 has 3 significant figures (5, 0 and 6).
- Keep the size of the number the same: 6482 to 1 s.f. is 6000, not 6.
Estimating
- Round every number to 1 significant figure, then calculate: 48 × 21 ≈ 50 × 20 = 1000.
- (6.1 × 49.8) ÷ 9.7 ≈ (6 × 50) ÷ 10 = 30.
- Estimate square roots using square numbers: √63.9 ≈ √64 = 8.
Over and underestimates
- If you round every number up in a multiplication, the estimate is an overestimate.
- If you round every number down, it is an underestimate.
- Dividing by a number that you rounded up gives a smaller answer, so be careful with division.
Key terms
- Rounding
- Writing a number approximately, to a given accuracy.
- Decimal places (d.p.)
- The number of digits after the decimal point.
- Significant figures (s.f.)
- The digits of a number starting from the first non-zero digit.
- Estimate
- An approximate answer, found by rounding.
- Overestimate
- An estimate that is bigger than the exact answer.
- Underestimate
- An estimate that is smaller than the exact answer.