A car moved 830 m in 39.6 s. Using the formula [math: speed=distance movedtime taken] calculate the speed of the car to the appropriate number of significant figures.

Question

BlackTom AI · Accepted Answer

Speed = distance / time, so compute 830 m ÷ 39.6 s.

Relevant concepts:
- The formula for average speed is speed = distance / time.
- For multiplication/division, the result should be reported with the same number of significant figures as the measurement with the fewest significant figures.
- Trailing zeros in a whole number without a decimal point are ambiguous; the usual convention is to treat 830 (no decimal shown) as having 2 significant figures (8 and 3) unless otherwise indicated.

Step-by-step calculation:
1. Compute the raw quotient:
   830 ÷ 39.6 = 20.95959595... m/s (20.96 m/s to 4 significant figures).
2. Determine significant figures to report:
   - distance 830 → assumed 2 significant figures
   - time 39.6 → 3 significant figures
   The least number is 2 significant figures, so the final answer must have 2 s.f.
3. Round 20.9596... to 2 significant figures:
   - The first two significant digits are "2" and "0" (i.e., 20). Look at the next digit (9) → rounds up.
   - 20 rounded to 2 s.f. with the next digit 9 becomes 21 (two significant figures).

Why this is correct:
- The computed value ~20.96 m/s is the precise quotient, but reporting must respect measurement precision. Given 830 has 2 s.f., the correct rounded value is 21 m/s.

Why other formats are not correct:
- Writing 20.96 m/s gives too many significant figures (four); it implies greater precision than the input distance supports.
- Writing 21.0 m/s would show three significant figures and would be appropriate only if 830 were specified to three significant figures (e.g., written 830. or 8.30×10^2); it is not in this problem.

Conclusion:
Rounded to the appropriate number of significant figures, the speed is 21 m/s, which matches the provided answer.

A car moved 830 m in 39.6 s. Using the formula [math: speed=distance movedtime taken] calculate the speed of the car to the appropriate number of significant figures.数值题

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