How many significant digits should be reported in the answer to the following calculation?
在以下计算的答案中应报告多少位有效数字？

(4.3 - 3.7) × 12.3 =
（4.3 - 3.7） × 12.3 =

Question

How many significant digits should be reported in the answer to the following calculation?
在以下计算的答案中应报告多少位有效数字？

(4.3 - 3.7) × 12.3 =
（4.3 - 3.7） × 12.3 =

BlackTom AI · Accepted Answer

Subtraction follows decimal-place rules: the result is limited by the least number of decimal places; multiplication/division follow significant-figure-count rules.

1. Relevant knowledge points and concepts
- For addition/subtraction, the number of decimal places (not total significant figures) in the result is limited by the operand with the fewest decimal places.
- For multiplication/division, the number of significant figures in the result is limited by the factor with the fewest significant figures.
- Significant figure counting: nonzero digits are always significant; leading zeros are not significant; trailing zeros may or may not be significant depending on context/notation.

2. Complete reasoning process step by step
- First perform the subtraction: 4.3 − 3.7.
  - Both numbers have 1 decimal place, so the subtraction result must be reported with 1 decimal place.
  - 4.3 − 3.7 = 0.6 (one decimal place).
- Determine significant figures of each factor for the multiplication:
  - 0.6 has 1 significant figure (the leading zero is not significant; only the digit 6 counts).
  - 12.3 has 3 significant figures (digits 1, 2, and 3).
- For multiplication, the result must have as many significant figures as the factor with the fewest significant figures: here, 1 significant figure.

3. Intermediate calculations
- 4.3 − 3.7 = 0.6
- 0.6 × 12.3 = 7.38 (raw product)
- Round 7.38 to 1 significant figure: look at first digit 7 and next digit 3 (<5), so it rounds to 7.

4. Why the correct answer is correct
- The subtraction step produces a factor with only 1 significant figure; multiplication requires that the final answer carry only 1 significant figure, so the correctly reported numerical result (with correct significant-figure rounding) is 7, i.e., one significant digit.

5. Why other counts would be incorrect
- Reporting 2 or 3 significant figures would violate the multiplication rule because one factor (0.6) only provides 1 significant figure. Using decimal-place rules from the subtraction step for the final multiplication is incorrect; multiplication uses sig-fig counts, not decimal places.

6. Conclusion
- The number of significant digits that should be reported is 1, which matches the provided answer.

How many significant digits should be reported in the answer to the following calculation? 在以下计算的答案中应报告多少位有效数字？ (4.3 - 3.7) × 12.3 = （4.3 - 3.7） × 12.3 =单项选择题

类似问题

How many significant digits are there in 0.000350 ?

Part 1Determine the number of significant digits in each of the given approximate numbers. 200200; 200.0200.0; 20 0 overbar200 Part 1The number of significant digits in 200200 is [input]22 .

Give the number of significant figures in each of the following: 2.30

How many significant digits are in the number: 730

How many significant digits are in the number: 0.0059

In a calculation, a scientist obtained the number 0.0008367070 on a calculator. If the number actually had five (5) significant figures, how should it be written?

What is the solution? 1.00×10−153.9×10−7\frac{1.00\times10^{-15}}{3.9\times10^{-7}} [Fill in the blank], x 10[Fill in the blank], Answer to y must have the correct number of significant figures.

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