Tag: significant figures and rounding of digits

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Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

Write down the significant figures in the following
1. $5238$ N
2. $4200 $kg

  1. $4 , 4$

  2. $4 , 2$

  3. $4, 3$

  4. $5, 3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
All non-zero digits are significant and last zeros are not considered as significant.
(a) : The given number $5238$ has four significant figures.
(b) : The given number $4200$ has two significant figures.
Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

if $L=2.331 cm$, $B = 2.1 cm$, then L+B=

  1. $4.431cm$

  2. $4.43cm$

  3. $4.5cm$

  4. $4.2cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Step 1
$L = 2.331 cm = 2.33$ (corrected to two decimal places) and $B = 2.1 cm$
Step 2
$L + B = 2.33 + 2.1 = 4.43cm. = 4.4cm$
(by the rule of addition the sum is expressed in minimum decimal places of terms in addition).
Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

A packet contains silver powder of mass $20.23g\pm 0l01g$. Some of the powder of mass $5.75g\pm 0.01g$ is taken out from it. The mass of the powder left back is

  1. $14.48g\pm 0.00g$

  2. $14.48g\pm 0.02g$

  3. $14.5g\pm 0.1g$

  4. $14.5g\pm 0.2g$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When subtracting values, the absolute uncertainties are added. 20.23 - 5.75 = 14.48, and 0.01 + 0.01 = 0.02.

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

The distance $s$ traveled by a particle in time $t$ is
$s=ut-\cfrac{1}{2}g{t}^{2}$
The initial velocity of the particle was measured to be $u=1.11\pm 0.01m/s$ and the time interval of the experiment was $t=1.01\pm 0.1s$. The acceleration was taken to be $g=9.8\pm 0.1m/{s}^{2}$. With these measurements, the student estimates the total distance traveled. How should the student report the result?

  1. $1.121\pm 0.m$

  2. $1.1\pm 0.1m$

  3. $1.12\pm 0.07m$

  4. $1.1\pm 0.07m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

The diameter and height of a cylinder are measured by a meter scale to be $12.6\pm 0.1$ cm and $34.2\pm 0.1$ cm ,respectively. What will be the value of its volume in appropriate significant figures?

  1. $4264\pm 81{ cm }^{ 3 }$

  2. $4260\pm 80{ cm }^{ 3 }$

  3. $4264.4\pm 81.0{ cm }^{ 3 }$

  4. $4300\pm 80{ cm }^{ 3 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume V = pi * r^2 * h. With diameter d = 12.6, r = 6.3. V = pi * (6.3)^2 * 34.2 = 4264.4. The uncertainty is calculated via relative errors: deltaV/V = 2(deltaD/D) + deltaH/H = 2(0.1/12.6) + 0.1/34.2 = 0.0158 + 0.0029 = 0.0187. deltaV = 4264.4 * 0.0187 = 79.7, which rounds to 81.