Calculation of permissible error in physical quantity

1. Mar 16, 2016

Abhishek Gupta

1. The problem statement, all variables and given/known data
I have doubt in calculating the permissible error. It goes as follows
Measure of two quantities along with the precision of respective measuring instrument is
A = 25.0 ± 0.5 m/s, B = 0.10 ± 0.01 s. A physical quantity C is calculated as C = A × B. What will be the value of C along with permissible error

2. Relevant equations
$\frac { ΔC } {C} = \Big ( {\frac { ΔA } {A} + \frac {Δ B} {B} } \Big )$

3. The attempt at a solution
STEP 1.
In the literature it is clearly mention that number of significant figures in result C is governed by the following rule.
"In multiplication or division, the final result should retain as many significant figures as are there in the original number with smallest number of significant figures."
Going by this rule C= 25.0 x 0.10 = 2.50 m = 2.5 m (rounding off to two significant figures).

STEP 2.
$\frac { ΔC } {C} = \Big ( {\frac { ΔA } {A} + \frac {Δ B} {B} } \Big ) = \Big ( {\frac { 0.5 } {25.0} + \frac {Δ0.01} {0.10} } \Big ) = 0.2 + 0.1 = 0.3$
ΔC = 0.3 × 2.5 =0.75 m
However, to what the significant figures after rounding off, the permissible error ΔC should be reported. Should ΔC=0.75m or 0.7m or something else What is the rule governing this?

Last edited: Mar 16, 2016
2. Mar 16, 2016

SammyS

Staff Emeritus
Have you made an error in (ΔA)/A ?

3. Mar 16, 2016

Abhishek Gupta

Respected Sir
With all due respect I did n't get you

4. Mar 16, 2016

SammyS

Staff Emeritus
It was a very direct question.

Restated: What is 0.5/25 ?

5. Mar 16, 2016

Abhishek Gupta

I apologize for the error . I have corrected it below.
STEP 2.

$\frac { ΔC } {C} = \Big ( {\frac { ΔA } {A} + \frac {Δ B} {B} } \Big ) = \Big ( {\frac { 0.5 } {25.0} + \frac {Δ0.01} {0.10} } \Big ) = 0.02 + 0.1 = 0.12$
ΔC = 0.12 × 2.5 =0.30 m
However, to what the significant figures after rounding off should the permissible error ΔC be reported. Should ΔC=0.30m or 0.3m or something else What is the rule governing this?

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