Question 6

MCQMEDIUM

Length, breadth and thickness of a strip having a uniform cross section are measured to be 10.510.5 cm, 0.050.05 mm, and 6.06.0 μ\mum, respectively. Which of the following option(s) give(s) the volume of the strip in cm3^3 with correct significant figures:

(A)

3.2×10−53.2 \times 10^{-5}

(B)

32.0×10−632.0 \times 10^{-6}

(C)

3.0×10−53.0 \times 10^{-5}

(D)

3×10−53 \times 10^{-5}

Detailed Solution

To find the volume V=L×B×TV = L \times B \times T, we first convert all measurements to the same unit (cm):

  • L=10.5L = 10.5 cm (3 significant figures)
  • B=0.05B = 0.05 mm =0.005= 0.005 cm (1 significant figure)
  • T=6.0T = 6.0 μ\mum =6.0×10−4= 6.0 \times 10^{-4} cm =0.00060= 0.00060 cm (2 significant figures)

Calculation: V=10.5×0.005×0.00060=0.0000315V = 10.5 \times 0.005 \times 0.00060 = 0.0000315 cm3^3.

According to the rules for significant figures in multiplication, the result must be rounded to the least number of significant figures found in the factors. The number of significant figures are 3, 1, and 2. The minimum is 1. Rounding 0.00003150.0000315 to 1 significant figure gives 0.000030.00003 cm3^3, which is 3×10−53 \times 10^{-5} cm3^3. Thus, option (D) is correct.

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