Tag: measurement and data processing and analysis

Quizzes (2) Questions (64)

Questions Related to measurement and data processing and analysis

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

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 :

  1. 4 grams

  2. 4.1 grams

  3. 4.139 grams

  4. 4.14 grams

  5. 4.140 grams
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. $4.18333$
  2. $4.2$
  3. $4.18$
  4. $4.183$

  5. 37.45
Reveal answer Fill a bubble to check yourself
B Correct answer
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, $\dfrac{12.55}{3.0}=4.2$

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

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

  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. $4.5\times {10}^{5}$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

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

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

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

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

  1. $4\times {10}^{37}$
  2. $3.69\times {10}^{37}$
  3. $3.7\times {10}^{37}$
  4. $3.69\times {10}^{40}$
  5. $3.7\times {10}^{40}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In multiplication, the result is reported to the same number of significant figures as the measurement with the fewest significant figures. Here, 3 * 10^14 has 1 significant figure, while 1.23 * 10^23 has 3. Therefore, the product must be rounded to 1 significant figure. Calculating 3.69 * 10^37 and rounding to one significant figure gives 4 * 10^37.

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

Select the numbers with same significant figures:

  1. $6.02 \times 10^{23}$
  2. $0.25$
  3. $6.60 \times 10^{-34}$
  4. $1.50$
Reveal answer Fill a bubble to check yourself
A,C,D Correct answer
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.

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

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

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
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.