Question

the length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significant figures and error is (A) 164 + 3 cm2 (B) 163.62 £ 2.6 cm2 (C) 163.6 + 2.6 cm2 (D) 163.62 + 3 cm.
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Answer 1

Given Length and breadth of a rectangular sheet are 16.2 cm and 10.1 CM respectively the area of the sheet in appropriate significant figures and error is

Let Δa = error in measurement of a

   Δb = error in measurement of b

   Δx = error in finding x

 Now maximum fractional error in x is  

So  Δx /x = (Δa/a + Δb/b)

Now given length = (16. cm^2 ± 0.1) cm

       Breadth = b = (10.1 ± 0.1) cm

        Area = l x b

                  = 16.2 x 10.1

                  = 163.62 sq cm

Now rounding off the area we get area = 164 sq cm

If ΔA is error in area, then relative error is given as ΔA/A = Δl/l ± Δb/b

      = 0.1/16.2 ± 0.1/10.1

      = 1.01 ± 1.62 / 163.62

       = 2.63 / 163.62

It implies ΔA = A x 2.63 / 163.62 sq cm

                      = 163.62 x 2.63 / 163.62

                      = 2.63 sq cm

By rounding off to one significant figure we get

ΔA = 3 sq cm

Now Area = A ± ΔA

                = (164 ± 3) sq cm

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