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Q1.31(i):
How many significant figures should be present in the answer of the following calculations? (i) $\frac{0.02856 \times 298.15 \times 0.112}{0.5785}$

Solution :

Step 1: Identification of Input Values and Significant Figures

To determine the number of significant figures in the result of multiplication and division, the rule is to round the final answer to the same number of significant figures as the number with the fewest significant figures in the calculation [Per the Rules for Significant Figures in Multiplication/Division].

Value Number of Significant Figures Justification
$0.02856$ 4 Leading zeros are not significant; digits 2, 8, 5, 6 are significant.
$298.15$ 5 All non-zero digits and zeros between them are significant.
$0.112$ 3 Leading zeros are not significant; digits 1, 1, 2 are significant.
$0.5785$ 4 Leading zero is not significant; digits 5, 7, 8, 5 are significant.

Step 2: Determining the Limiting Factor

We compare the significant figures identified in Step 1:

  • $0.02856 \rightarrow 4 \text{ s.f.}$
  • $298.15 \rightarrow 5 \text{ s.f.}$
  • $0.112 \rightarrow 3 \text{ s.f.}$
  • $0.5785 \rightarrow 4 \text{ s.f.}$
The value with the minimum number of significant figures is $0.112$, which contains 3 significant figures.

Step 3: Logical Application of the Rule

The precision of the final product/quotient is limited by the least precise measurement. Since the least precise term ($0.112$) has 3 significant figures, the final result must be rounded to 3 significant figures to maintain scientific integrity [Per the Convention of Significant Figures].

Calculation Analysis: Input Constraints: {4, 5, 3, 4} s.f. | Min(Constraints) = 3 s.f. Result must be expressed to 3 significant figures.

Final Solution: The answer should be reported with 3 significant figures.


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