3. Calculate the answers to the appropriate number of significant figures. a) 23.7 \times 3.8 = e) 43.678 \times 64.1 = b) 45.76 \times 0.25 = f) 1.678 / 0.42 = c) 81.04 \times 0.010 = g) 28.367 / 3.74 = d) 6.47 \times 64.5 = h) 4278 / 1.006 =
The Correct Answer and Explanation is:
Answers with Correct Significant Figures:
a) 23.7 × 3.8 = 90
b) 45.76 × 0.25 = 11
c) 81.04 × 0.010 = 0.81
d) 6.47 × 64.5 = 418
e) 43.678 × 64.1 = 2800
f) 1.678 ÷ 0.42 = 4.0
g) 28.367 ÷ 3.74 = 7.58
h) 4278 ÷ 1.006 = 4252
Explanation
When performing multiplication or division with measurements, the result should be rounded to reflect the precision of the least precise value used in the calculation. This is known as following the significant figures rule. Significant figures are digits that carry meaning contributing to a number’s precision. These include all non-zero digits, any zeros between significant digits, and any trailing zeros in a decimal number.
In multiplication and division, the number of significant figures in the final result should be the same as that of the factor with the fewest significant figures. This principle ensures that the result does not suggest greater accuracy than the input data justifies.
For example, in part (a), 23.7 (3 significant figures) × 3.8 (2 significant figures) results in 89.94. Since 3.8 has the fewest significant figures (2), the final result is rounded to 90, which has 2 significant figures.
Similarly, in part (e), 43.678 (5 sig figs) × 64.1 (3 sig figs) gives 2799.4298. Rounded to 3 significant figures, the result becomes 2800. Note that trailing zeros in a non-decimal number are not considered significant unless indicated by a decimal point or scientific notation.
In division, like in part (f), 1.678 ÷ 0.42 = 3.9952. The number with the fewest sig figs is 0.42 (2 sig figs), so the result is rounded to 4.0, preserving the precision.
Using significant figures maintains the integrity of experimental and measured data, avoiding overstating the precision of results derived from such data.
