Tag: measurement and data processing and analysis

Questions Related to measurement and data processing and analysis

Two samples were weighed using different balance and the following data were obtained.
Sample #1=3.719 grams
Sample #2=0.42 gram
The total mass of the samples should be reported as :

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. 4 grams

  2. 4.1 grams

  3. 4.139 grams

  4. 4.14 grams

  5. 4.140 grams

Show answer
Correct Option: D
Explanation:

After rounding off to $2$ significant digits, weight of sample $1$ can be reported as $3.72$ grams. Therefore, total mass $= (3.72+0.42)=4.14 $ grams.

What is the final significant digit in the measurement of $16.280g$?

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. $1$

  2. $0$

  3. $8$

  4. $6$

  5. $2$

Show answer
Correct Option: B
Explanation:

The significant digits in the number $16.280$ are $1,6,2,8$ and $0$. Therefore, the final significant digit in the given number is $0$.

Which choice shows the answer to the following mathematical operation with the correct number of significant figures?
$\dfrac{12.55}{3.0} =4.18333$

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. $4.18333$

  2. $4.2$

  3. $4.18$

  4. $4.183$

  5. 37.45

Show answer
Correct Option: B
Explanation:

In multiplication, the final answer is reported as the same number of decimal places as that of the number with the least decimal places.

Therefore, $4.18333$ should be rounded off to only one decimal place.
Therefore, $\dfrac{12.55}{3.0}=4.2$

Which choice shows the answer to the following mathematical operation with the correct number of significant figures?
$4.51\times{10}^{5}+3.6\times{10}^{3}$

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. $4.55\times {10}^{5}$

  2. $8.11\times {10}^{5}$

  3. $4.546\times {10}^{5}$

  4. $8.11\times {10}^{8}$

  5. $4.5\times {10}^{5}$

Show answer
Correct Option: E
Explanation:

In addition, the final product is reported as the same number of decimal places as that of the number with least decimal places.

$\therefore \quad 4.51\times { 10 }^{ 5 }+3.6\times { 10 }^{ 3 }=4.546\times { 10 }^{ 5 }$
                                                  $=4.5\times 10^5$

What is the molecular mass of glucose $C _6H _{12}O _6$ molecule up to 6 significant figures?

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. 0180.16

  2. 180.16

  3. 180.1620

  4. 180.162

Show answer
Correct Option: D
Explanation:

Molecular mass of glucose is $180.162$

Therefore, the molecular mass upto six significant figures is $180.162$.

Which choice shows the answer to the following mathematical operation with the correct number of significant figures?
$(1.23\times {10}^{23})\times (3\times{10}^{14})=3.69\times {10}^{37}$

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. $4\times {10}^{37}$

  2. $3.69\times {10}^{37}$

  3. $3.7\times {10}^{37}$

  4. $3.69\times {10}^{40}$

  5. $3.7\times {10}^{40}$

Show answer
Correct Option: C

Which of the following is an exact number?

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. 10.25 g

  2. 4.000 kg

  3. 7 chairs

  4. 60 seconds

Show answer
Correct Option: C
Explanation:

Exact number is the number which does not have uncertainity in measurement and significant figures.

Therefore, $7$ chairs is an exact number.

Select the numbers with same significant figures:

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. $6.02 \times 10^{23}$

  2. $0.25$

  3. $6.60 \times 10^{-34}$

  4. $1.50$

Show answer
Correct Option: A,C,D
Explanation:

In $A:-$ Significant figures $=6,0,2 \Rightarrow 3$ figures

In $B:-$ Significant figures $=2,5 \Rightarrow 2$ figures
In $C:-$ Significant figure $=6,6,0 \Rightarrow 3$ figures
In $D:-$ Significant figures $=1,5,0 \Rightarrow 3$ figures
Therefore, $(A), (C)$ and $(D)$ have same significant figure.

In which of the following numbers, all the zeros are insignificant?

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. 0.0010

  2. 0.00100

  3. 0.001000

  4. 0.001

Show answer
Correct Option: D
Explanation:

All the last zero or trailing zero's in the decimal portion and between 2 significant digits only are significant.

Which set of figures will be obtained after rounding up the following upto three significant figures?
34.216,  0.04597, 10.4107

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. 34.3, 0.0461, 10.4

  2. 34.2, 0.0460, 10.4

  3. 34.20, 0.460, 10.40

  4. 34.21, 4.597, 1.04

Show answer
Correct Option: B
Explanation:

To round up a given number, ignore the last digit as such if the digit next to it is less than 5. Then increase it by 1, if the next digit is greater than 5.

(i) 34.216

34.22 { since next digit (6) is greater than 5 }

34.2 {since next digit (2) is less than 5 }

 (ii) 0.04597

0.0460 {since next digit (7) is greater than 5}

(iii) 10.4107

10.411 { since next digit (7) is greater than 5}

10.41 { since next digit (1) is less than 5}

10.4 { since next digit (1) is less than 5}

Thus option B is correct.