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

The radius of sphere is measured to be $\displaystyle \left ( 2.1\pm 0.5 \right )$cm.
 Calculate its surface area with error limits.

  1. $\displaystyle S=\left ( 55.4\pm 26.4 \right )cm^{2}$

  2. $\displaystyle S=\left ( 55.4\pm 26.4 \right )mm^{2}$

  3. $\displaystyle S=\left ( 55.4\pm 13.2 \right )cm^{2}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Surface area, $\displaystyle S=4\pi r^{2}=\left ( 4 \right )\left ( \frac{22}{7} \right )\left ( 2.1 \right )^{2}$$\displaystyle =55.44=55.4cm^{2}$
Further, $\displaystyle \frac{\Delta S}{S}=2.\frac{\Delta r}{r}$
              $\displaystyle \Delta S=2\left ( \frac{\Delta r}{r} \right )\left ( S \right )=\frac{2\times 0.5\times 55.4}{2.1}$$\displaystyle =26.38=26.4 cm^{2}$

$\displaystyle \therefore S=\left ( 55.4\pm 26.4 \right )cm^{2}$

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

Find density when a mass of 9.23 kg occupies a volume of $\displaystyle 1.1m^{3}$ with due regard to significant figures.

  1. $\displaystyle 8.4 kg/m^{3}$

  2. <span>$\displaystyle 8.39 kg/m^{3}$</span>

  3. <span>$\displaystyle 8.3 kg/m^{3}$</span>

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mass $= 9.23\ kg$ .... 3 significant figures

Volume $= 1.1\  m^3$ .... 2 significant figures

Therefore, $density = mass/volume = 8.4\ kg/m^3$ 

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

The value due regard to significant figure  $ 4.0\times 10^{-4}-2.5\times 10^{-6}$ 

  1. $\displaystyle 4.0\times 10^{-4}$

  2. <span>$\displaystyle 3.975\times 10^{-4}$</span>

  3. <span>$\displaystyle 3.9\times 10^{-4}$</span>

  4. none of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The value of this case is,
$4.0\times 10^{-4}-2.5\times 10^{-6}$
$=3.975\times 10^{-4}$.
Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

Length, breadth and thickness of a rectangular slab are 4.234 m, 1.005 m and 2.01 m respectively. Find volume of the slab to correct significant figures.

  1. $\displaystyle 8.55 m^{3}$

  2. <span>$\displaystyle 8.552 m^{3}$</span>

  3. <span>$\displaystyle 8.6 m^{3}$</span>

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

l = 4.234 m 4 significant figures

b = 1.005 m 4 significant figures
w = 2.01 m 3 significant figures 
Therefore, Volume = lbw= 8.55 .........3 significant figures