Tag: significant figures

Questions Related to significant figures

Write down the number of significant figures in the following.
$6428$

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

  1. $four$

  2. $three$

  3. $two$

  4. $one$

Show answer
Correct Option: A
Explanation:

For a number with $NO \ \ ZERO$ to the right, the number of significant figures is simply the total number of digits.

Here the total significant figures is $4$.

The area of rectangle of size 1.23cm $ \times $ 2.345cm is ?

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

  1. $ 2.88cm^2 $

  2. $ 2.884cm^2 $

  3. $ 2.9cm^2 $

  4. $ 2.88435cm^2 $

Show answer
Correct Option: A
Explanation:

$1.23\times 2.345=2.88$

Since final answer should be expressed in 3 significant figures because least number of significant figures in question are 3.

The significant digits in 200.40 are ?

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

  1. 4

  2. 5

  3. 2

  4. 3

Show answer
Correct Option: B
Explanation:

All the digits in 200.40 are significant since zeroes after non zero digit after decimal are significant . 

Therefore, (B) 5 is correct answer.

The mass of a beaker is found to be ($10.1 \pm 0.1)gm $ when empty and $(17.3 \pm 0.1)gm$ when partially filled with a liquid. What is the best value for the mass of the liquid together with the possible limits of accuracy?

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

  1. $(7.2  \pm 0.2)gm$

  2. $(7.2  \pm  0.1)gm$

  3. $(7.1  \pm  0.2)gm$

  4. $(7.2  \pm  0.3)gm$

Show answer
Correct Option: B
Explanation:

Here mass of the liquid , $m=m _2-m _1=17.3-10.1=7.2 gm$

So the relative error, $\dfrac{\Delta m}{m}=\pm\left[\dfrac{\Delta m _1}{m _1}+\dfrac{\Delta m _2}{m _2}\right]$
or $\Delta m=\pm\left[\dfrac{\Delta m _1}{m _1}+\dfrac{\Delta m _2}{m _2}\right]\times m=\pm[0.1/10.1+0.1/17.3]\times 7.2=\pm 0.1 gm$
Thus mass of liquid with possible accuracy $=(7.2\pm 0.1) gm$

Measure of two quantities along with the precision of respective measuring instrument is:
$A = 2.5 ms^{-1}\pm 0.5 ms^{-1}$
$B = 0.10s \pm 0.01 s$
The value of AB will be :

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

  1. $(0.25\pm 0.08)m$

  2. $(0.25\pm 0.5)m$

  3. $(0.25\pm 0.05)m$

  4. $(0.25\pm 0.135)m$

Show answer
Correct Option: A
Explanation:

Given :  $\Delta A = 0.5 \ m/s$        $\Delta B = 0.01 \ s$

The absolute value of AB  $ = 2.5\times 0.10 = 0.25 \ m$

Relative error in AB,    $\dfrac{\Delta AB}{AB} = \dfrac{\Delta A}{A} +\dfrac{\Delta B}{B}$

$\therefore$   $\dfrac{\Delta AB}{0.25} = \dfrac{0.5}{2.5} +\dfrac{0.01}{0.10}$

$\implies \ \Delta AB = 0.075 = 0.08 \ m$
Thus value of AB is  $(0.25\pm0.08) \ m$

Count total number of S.F. in 300.00

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

  1. 5

  2. 6

  3. 8

  4. 9

Show answer
Correct Option: A
Explanation:

S.F. = Five, trailing zeros after decimal point are significant.

Count total number of significant figures in 0.00418

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

  1. 5

  2. 4

  3. 3

  4. 6

Show answer
Correct Option: C
Explanation:

S.F. = Three, as leading  zeros are not significant.

Count total number of Significant Figures in 3.0800

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

  1. 3

  2. 5

  3. 1

  4. 2

Show answer
Correct Option: B
Explanation:

S.F. = Five, as trailing zeros after decimal place are significant.

Count total number of significant figures in 3500

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

  1. 1

  2. 2

  3. 3

  4. 4

Show answer
Correct Option: B
Explanation:

S.F. = Two , the trailing zeros are not significant.

Count total number of S.F. in $1.60\, \times\, 10^{- 19}$ 

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

  1. 3

  2. 5

  3. 2`

  4. 22

Show answer
Correct Option: A
Explanation:

S.F. = Three ; 1, 6, 0; remaining 19 zeros are not significant.