Tag: units and measurements

Questions Related to units and measurements

Count total number of S.F. in 5.003020

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

  1. 3

  2. 20

  3. 7

  4. 9

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Correct Option: C
Explanation:

S.F. = Seven, the trailing zeros after decimal place are significant.

Count total number of S.F. in $6.020\, \times\, 10^{23}$

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

  1. 4

  2. 3

  3. 6

  4. 7

Show answer
Correct Option: A
Explanation:

S.F. = Four; 6, 0, 2, 0; remaining 23 zeros are not significant.

If accuracy of weighing machine is better than 1/2 percent, a student record his own mass. Choose the option that explains the recording most accurately.

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

  1. 6.43 kg

  2. 60 kg

  3. 64.3 kg

  4. 600kg

  5. 643 kg

Show answer
Correct Option: C
Explanation:

This question is intended to assess your knowledge of realistic values for physical quantities as well as an understanding of experimental error and significant figures. Only 60 kg and 64.3 kg are likely masses for an adult human. When recording measurements, it is assumed that there is some measurement error in the last digit recorded. For both possible values for the student's weight, 1/2 percent is about 0.3 kg. Therefore, a mass recorded to better than this accuracy will indicate tenths of a kilogram.

The length,breadth and thickness of a rectangular copper sheet are $4 cm, 2.5 cm $ and $1.56 cm $ respectively. Find the area of the sheet to corrected significant figures.

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

  1. $40.3 cm^2$

  2. $40.28 cm^2$

  3. $40 \times 10^2 cm^2$

  4. $0.4\times 10^2 cm^2$

Show answer
Correct Option: D
Explanation:

If $l$ be the length, $b$ be the breadth and $t$ be the thickness of the sheet,
then the area of sheet is $A=2(lb+bt+tl)=2[(4\times 2.5)+(2.5\times 1.56)+(1.56\times 4)]=40.28 cm^2$
As length has least significant figures i.e one so the answer must be expressed as one significant figures. 
Thus according rule of determining significant figures, the area will be $0.4\times 10^2 cm^2$

The number of significant figures in 500.06 is ________.

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

  1. 2

  2. 3

  3. 5

  4. 0

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Correct Option: C
Explanation:

All non-zero digits and zeros between non-zero digits are considered as significant figures. Thus the number $500.06$ has $5$ significant digits.

Express 0.006006 into scientific notation in three significant digits:

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

  1. $6.01 \times 10^{-3}$

  2. $6.0006 \times 10^{-3}$

  3. $6.00 \times 10^{-3}$

  4. $6.0 \times 10^{-3}$

Show answer
Correct Option: A
Explanation:
The number  $0.006006$ has 6 significant figures.
We need to round off the given number to convert into 3 significant figure. Thus,  the correct answer is  $6.01\times 10^{-3}$ as it has 3 significant figure including rounding off.

Which of the following quantifies has the least number of significant digits? 

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

  1. $0.80760 $

  2. $0.08765$

  3. $5.7423 \times 10^2$

  4. $80.760$

Show answer
Correct Option: B
Explanation:
The number $0.80760$ has $5$ significant digits, $0.08765$ has $4$ significant digits, $5.7423\times 10^{2}$ has $5$ significant digits and $80.760$ has $5$ significant digits.
Hence option B is correct.

A person was weighing $102.1\  kg$ last week and gained $0.28 \ kg$ this week. His weight as of now is correctly expressed as :

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

  1. $102.38\  kg$

  2. $102.3\  kg$

  3. $102.4\  kg$

  4. $102\  kg$

Show answer
Correct Option: C
Explanation:

We know that number of significant figures after addition will be equal to least number of significant figures present in any of the operand.
Therefore total weight after weight gain is $102.1+0.28=102.38 kg$
Now least number of significant figure present after the decimal in the operand is 1, present in $102.1\ kg$ .
Therefore, the number of significant figures present after the calculation should also be $1$ after the decimal. Hence, when we round the answer $102.38$ becomes $102.4\  kg$
Therefore correct answer is option (C)

Subtract $3.2 \times 10^{-6}$ from $4.7 \times 10^{-4}$ with due regard to significant figures.

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

  1. $~4.7 \times 10^{-4}$

  2. $~7 \times 10^{-4}$

  3. $~5.7 \times 10^{-4}$

  4. $~4.7 \times 10^{-5}$

Show answer
Correct Option: A
Explanation:

$4.7\times { 10 }^{ -4 }-3.2\times { 10 }^{ -6 }$

$=4.7\times { 10 }^{ -4 }-0.032\times { 10 }^{ -4 }$
$=4.668\times { 10 }^{ -4 }\approx 4.7\times { 10 }^{ -4 }$.

Subtract $1.5 \times 10^3$ from $4.8 \times 10^4$ with due regard to significant figures.

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

  1. $~4.6 \times 10^{4}$

  2. $~4.6 \times 10^{5}$

  3. $~4.6 \times 10^{6}$

  4. $~5 \times 10^{4}$

Show answer
Correct Option: A
Explanation:

$4.8\times { 10 }^{ 4 }-1.5\times { 10 }^{ 3 }$

$=4.8\times { 10 }^{ 4 }-0.15\times { 10 }^{ 4 }$
$\Rightarrow 4.65\times { 10 }^{ 4 }\approx 4.7\times { 10 }^{ 4 }$