Source: Extra Practice

A physical quantity XX is calculated as X=a2bc3X = \frac{a^2 b}{c^3}. If the measured values are a=2.0a = 2.0, b=3.00b = 3.00, and c=1.000c = 1.000, find the value of XX to the correct number of significant figures.

Options

Option A is correct

1212

Option B

12.012.0

Option C

12.0012.00

Option D

12.00012.000

Explanation

Calculating the value: X=(2.0)2×3.00(1.000)3=4.0×3.001.000=12X = \frac{(2.0)^2 \times 3.00}{(1.000)^3} = \frac{4.0 \times 3.00}{1.000} = 12. For multiplication and division, the result must possess the same number of significant figures as the term with the fewest significant figures. The component 'a' (2.02.0) has 2 significant figures, 'b' (3.003.00) has 3, and 'c' (1.0001.000) has 4. Therefore, the result must have exactly 2 significant figures, which is represented by 1212.