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Which choice best describes the degree of uncertainty in the measurement of 16.30 g?(a) The uncertainty cannot be determined without additional information(b) The quantity is exact (c) + 0.10 g (d) + 0.01 g |
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Answer» Answer: Correct option is A 164±3cm 2
Error in product of QUANTITIES: SUPPOSE x=a×b Let Δa=absolute error in measurement of a, Δb=absolute error in measurement of b, Δx=absolute error in calculation of x, i.e. product of a and b. The maximum fractional error in x is x Δx
=±( a Δa
+ b Δb
) Percentage error in the value of x=(Percentage error in value of a)+(Percentage error in value of b) According to the problem, LENGTH l=(16.2±0.1)cm Breadth b=(10.1±0.1)cm Area A=l×b=(16.2cm)×(10.1cm)=163.62cm 2
As per the rule area will have only three significant FIGURES and error will have only one significant figure.ROUNDING off we get,area A=164cm 2
If ΔA is error in the area, then relative error is calculated as A δ4
. A Δ4
= l Δl
+ b Δb
= 16.2cm 0.1cm
+ 10.1cm 0.1cm
= 16.2×10.1 1.01+1.62
= 163.62 2.63
⇒ΔA=A× 163.62 2.63
cm 2 =162.62× 163.62 2.63
=2.63cm 2
ΔA=3cm 2 (By rounding off to one significant figure) Area, A=A±ΔA(164±3)cm 2 |
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