Tag: rounding of digits

Questions Related to rounding of digits

1 $\mathring{A}$ is equal to :

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

  1. $0.1$ nm

  2. $10^{-10}$ cm

  3. $10^{-8} m$

  4. $10^{-4} \mu$.

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Correct Option: A
Explanation:

1 Angstorm = $1 \times 10^{-10} $ m = $0.1 \ nm$  ($10^{-9}$ m)

The thickness of a metal sheet is measured to be $326 mm$. Express its order of magnitude in mm.

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

  1. $10^0$

  2. $10^1$

  3. $10^2$

  4. $10^3$

Show answer
Correct Option: C
Explanation:

Thickness $t = 326\ mm$

                     $= 3.26 \times 10^2\ mm$
Hence, order of magnitude in mm is $10^2$.

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

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

  1. 242

  2. 243

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

  4. $24.2\times { 10 }^{ 3 }$

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Correct Option: D
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 $=24.2\times 10^{3}$

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

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

  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 $\times{ 10 }^{ -4 }$

Show answer
Correct Option: B
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 $\Rightarrow 3.12\times 10^{-4}$

The prefix used for denoting an order of magnitude of $\displaystyle { 10 }^{ 6 }$ is ___________.

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

  1. Giga

  2. Kilo

  3. Mega

  4. Micro

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Correct Option: C
Explanation:
Mega is the prefix used for denoting an order of magnitude of $10^6$.
For example :  $10^6\ Watt$ is also termed as $Megawatt$

State whether the following statement is True or False. 

The prefix used for $\displaystyle { 10 }^{ 3 }$ is kilo.

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

  1. True

  2. False

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Correct Option: A
Explanation:

The prefix used for $\displaystyle { 10 }^{ 3 }$ is kilo and it means 1000.

The thickness of a newspaper sheet is of the order of 

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

  1. 0.1 m

  2. 0.1 cm

  3. 0.1 mm

  4. 1 micrometre

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Correct Option: C
Explanation:

In general normal newspaper are in the order of 0.1 mm, but if some time in magazines the thickness may be order of 0.1 cm.

Which of the following represent the number 300,000,000 :

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

  1. $3 \times  10^6$

  2. $3 \times  10^7$

  3. $3 \times  10^8$

  4. $3 \times  10^9$

  5. $3 \times  10^{-9}$

Show answer
Correct Option: C
Explanation:

The given number:   

$300,000,000  =3 \times 10^8$

$1$ femtometre is equivalent to 

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

  1. $10^{15} m$

  2. $10^{-12} m$

  3. $10^{-15} m$

  4. $10^{-9} m$

Show answer
Correct Option: C
Explanation:

$1 $ femtometre $=10^{-15} m$

What is the order of magnitude of one light year? 

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

  1. $10^{15} m$

  2. $10^{10} m$

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

  4. $10^{16} m$

Show answer
Correct Option: D
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 $=10\times 10^{15}=10^{16} m$