What is called as relative error? Define fractional error.
(N/A) Relative error is defined as the ratio of the mean absolute error to the mean value of the quantity measured.
Mathematically,it is expressed as: $\text{Relative Error} = \frac{\Delta a_{\text{mean}}}{a_{\text{mean}}}$.
Fractional error is another term used for relative error. It represents the uncertainty in a measurement relative to the size of the measurement itself. When the relative error is expressed in percentage,it is called percentage error,given by: $\text{Percentage Error} = \frac{\Delta a_{\text{mean}}}{a_{\text{mean}}} \times 100\%$.
Mathematically,it is expressed as: $\text{Relative Error} = \frac{\Delta a_{\text{mean}}}{a_{\text{mean}}}$.
Fractional error is another term used for relative error. It represents the uncertainty in a measurement relative to the size of the measurement itself. When the relative error is expressed in percentage,it is called percentage error,given by: $\text{Percentage Error} = \frac{\Delta a_{\text{mean}}}{a_{\text{mean}}} \times 100\%$.
Explore More
Similar Questions
If $\theta_1 = 25.5 \pm 0.1 \, ^\circ C$ and $\theta_2 = 35.3 \pm 0.1 \, ^\circ C$,find $\theta_1 - \theta_2$.
Easy
View SolutionWhat is the percentage error in the measurement of the time period of a pendulum if the maximum errors in the measurement of $l$ and $g$ are $2\%$ and $4\%$ respectively?
Difficult
View SolutionIf the error in measuring the diameter of a circle is $4\%$,the error in the radius of the circle would be (in $\%$)
Easy
View Solution$A$ physical quantity $Q$ is related to four observables $a, b, c, d$ as follows: $Q = \frac{ab^4}{cd}$,where $a = (60 \pm 3) \ Pa$,$b = (20 \pm 0.1) \ m$,$c = (40 \pm 0.2) \ Nsm^{-2}$,and $d = (50 \pm 0.1) \ m$. The percentage error in $Q$ is $\frac{x}{1000}$,where $x = $ . . . . . . .
$A$ student determined Young's Modulus of elasticity using the formula $Y = \frac{M g L^{3}}{4 b d^{3} \delta}$. The value of $g$ is taken to be $9.8 \, m/s^2$, without any significant error. His observations are as follows:
Physical Quantity Least count and Observed value Mass $(M)$ $1 \, g$ and $2 \, kg$ Length of bar $(L)$ $1 \, mm$ and $1 \, m$ Breadth of bar $(b)$ $0.1 \, mm$ and $4 \, cm$ Thickness of bar $(d)$ $0.01 \, mm$ and $0.4 \, cm$ Depression $(\delta)$ $0.01 \, mm$ and $5 \, mm$
Then the fractional error in the measurement of $Y$ is:
| Physical Quantity | Least count and Observed value |
| Mass $(M)$ | $1 \, g$ and $2 \, kg$ |
| Length of bar $(L)$ | $1 \, mm$ and $1 \, m$ |
| Breadth of bar $(b)$ | $0.1 \, mm$ and $4 \, cm$ |
| Thickness of bar $(d)$ | $0.01 \, mm$ and $0.4 \, cm$ |
| Depression $(\delta)$ | $0.01 \, mm$ and $5 \, mm$ |
Then the fractional error in the measurement of $Y$ is:
DifficultJEE MAIN 2021
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo