Tag: units and measurement: error analysis

Questions Related to units and measurement: error analysis

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:

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

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

Add $3.8 \times 10^{-6} to 4.2 \times 10^{-5}$ with due regard to significant figures.

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

  1. $~4.6 \times 10^{-5}$

  2. $~4.6 \times 10^{-6}$

  3. $~5.6 \times 10^{-6}$

  4. $~6.6 \times 10^{-5}$

Show answer
Correct Option: A
Explanation:

$3.8\times { 10 }^{ -6 }+42\times { 10 }^{ -6 }=45.8\times { 10 }^{ -6 }=4.58\times { 10 }^{ -5 }$

                                                                      $=4.6\times { 10 }^{ -5 }$.

The radius of the earth is $6.37 \times 10^6 m$ and its mass is $5.975 \times 10^{24} kg$. Find the earth's average density to appropriate significant figures.

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

  1. $5 \times 10^3 kg m^{-3}$

  2. $5.52 \times 10^3 kg m^{-3}$

  3. $2 \times 10^3 kg m^{-3}$

  4. $5.52 \times 10^3 kg m^{-4}$

Show answer
Correct Option: B

The number of significant figures in $5.69 \times 10^{15}$kg is

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

  1. $1$

  2. $2$

  3. $3$

  4. $18$

Show answer
Correct Option: C
Explanation:

No. of significant figures in $\underbrace { 5.69 } \times { 10 }^{ 15 }$ Kg is $3$.

                                           Digits that cannot meaning to measurement and measurement resolution.