Tag: rounding off digits

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Multiple choice physics units and measurement: error analysis rounding off digits rounding of digits standard form

When $24.25\times { 10 }^{ 3 }$ is rounded off to three significant figures, it becomes :

  1. 242

  2. 243

  3. $244\times { 10 }^{ 2 }$

  4. $24.2\times { 10 }^{ 3 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$24.25\times 10^{3} \rightarrow 2,4,2,5\rightarrow $ present by it has 4 significant digits.
If the digit to be dropped is 5 or 5 followed by zeros, then preceding digit is left unchanged, if it is even.
So, up to three significant figures, the number $=24.2\times 10^{3}$

Multiple choice physics units and measurement: error analysis rounding off digits rounding of digits standard form

Two numbers are given as i) 20.96 and ii) 0.0003125. Rounding off above numbers to 3 significant figures will lead to :

  1. i) 21.0, ii) 312

  2. i) 21.0, ii) 3.12 $\times{ 10 }^{ -4 }$

  3. i) 2.10, ii) 3.12 $\times{ 10 }^{ -4 }$

  4. i) 210, ii) 3.12 $\times{ 10 }^{ -4 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

a) 20.96
We have to round off for 3 significant digits. Last digit has to be rounded off.
If the digit to be dropped (6) is more than 5, then preceding digit is raised by 1.
Hence  $20.96\approx 21.0$


b) $0.0003125=3.125\times 10^{-4}$
For 3 significant digits $\Rightarrow 3.12\times 10^{-4}$

Multiple choice physics units and measurement: error analysis rounding off digits rounding of digits standard form

What is the order of magnitude of one light year? 

  1. $10^{15} m$

  2. $10^{10} m$

  3. $9.2 \times 10^{15} m$

  4. $10^{16} m$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

One light year is the distance of light at a speed $3\times 10^8 m/s$ in 1 year. 
Thus, $1 $ light year $= 3\times 10^8 m/s\times 1$ year $=3\times 10^8 m/s\times (365\times 24\times 3600 s)=9.5\times 10^{15} m$
According to rule of order of magnitude, as $9.5>5$ so 9.5 will be taken as 10.
Thus, order of magnitude of one light year $=10\times 10^{15}=10^{16} m$