MathematicsExam code: 0580
Rounding, Estimation and Bounds
Number
Making the estimate
- Rounding every value to one significant figure turns an awkward calculation into one that can be done mentally
- 19.4 becomes 20 and 4.7 becomes 5
- When the question says 1 significant figure, round to exactly that, even where another rounding would make the arithmetic simpler
- Never round a value to zero: a zero denominator makes the calculation undefined, and a zero numerator destroys the estimate
Deciding whether the estimate is too big or too small
- For a sum or a product, rounding both values the same way settles it
| Operation | Both rounded up | Both rounded down |
|---|---|---|
| a + b | Overestimate | Underestimate |
| a × b | Overestimate | Underestimate |
- For a difference or a quotient the second value works in the opposite direction
| Operation | a up, b down | a down, b up |
|---|---|---|
| a − b | Overestimate | Underestimate |
| a ÷ b | Overestimate | Underestimate |
- Where the two roundings pull opposite ways, the direction cannot be decided without more care
Worked example
Estimating and judging the direction
Estimate the value of 19.4 × 4.7, and state whether the estimate is too large or too small.
Solution:
- Round each value to one significant figure: 19.4 becomes 20 and 4.7 becomes 5
- Multiply the rounded values: 20 × 5 = 100
- The estimate is 100
- Both values were rounded up, and this is a product, so the estimate is an overestimate
- The exact value is 91.18, which confirms the direction