The big idea: If a number is rounded, the true value lies in an interval around it.
Worked example
A length is given as 6.4 cm correct to 1 decimal place. Find the bounds.
Step by step
- 1 decimal place means nearest 0.1, so half a step is 0.05.
- Subtract and add 0.05.
Final answer
6.35 ≤ L < 6.45
Inclusive lower, exclusive upper: Use ≤ on the lower bound and < on the upper bound for standard rounding intervals.
Worked example
A mass is 370 g correct to 2 significant figures. Find the bounds.
Step by step
- 2 significant figures here means rounded to the nearest 10 g.
- Half a step is 5 g.
Final answer
365 ≤ m < 375
Look at place value first: With significant figures, first decide what place value the last kept digit is in.
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| Rounded value | Accuracy | Bounds |
|---|---|---|
| 8 cm | nearest cm | 7.5 ≤ x < 8.5 |
| 2.7 s | 1 d.p. | 2.65 ≤ t < 2.75 |
| 540 | 2 s.f. | 535 ≤ n < 545 |
Always include units when appropriate: If the quantity is in cm, kg, or seconds, keep the units with your interval statement.
Why bounds matter: In real problems, bounds help you work out best-case and worst-case possibilities from rounded measurements.
Worked example
A time is 12.6 s correct to 1 decimal place. What is the greatest possible true time?
Step by step
- Bounds are 12.55 ≤ t < 12.65.
- So the greatest possible true time is just less than 12.65 s.
Final answer
Upper bound 12.65 s