# Calculation of permissible error in physical quantity

## Homework Statement

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

## Homework Equations

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

## 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:

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

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

## Homework Equations

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

## 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.
$\frac { ΔC } {C} = \Big ( {\frac { ΔA } {A} + \frac {Δ B} {B} } \Big ) = \Big ( {\frac { 0.5 } {25.0} + \frac {Δ0.01} {0.10} } \Big ) = 0.2 + 0.1 = 0.3$
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?
Have you made an error in (ΔA)/A ?

Have you made an error in (ΔA)/A ?
Respected Sir
With all due respect I did n't get you

SammyS
Staff Emeritus
Homework Helper
Gold Member
Respected Sir
With all due respect I did n't get you
It was a very direct question.

Restated: What is 0.5/25 ?

It was a very direct question.

Restated: What is 0.5/25 ?

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?