This set of Bioprocess Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Errors in Data and Calculations”.

1. What is the rounding off of a number?

a) To change a number to its nearest prime number

b) To change a number to its nearest odd number

c) To change a number to its nearest whole number

d) To change a number to its nearest even number

View Answer

Explanation: To reduce successively the number of digits to the right of the decimal point of a mixed number by dropping the final digit and adding 1 to the next preceding digit if the dropped digit was 5 or greater, or leaving the preceding digit unchanged if the dropped digit was 4 or less.

2. Round off the number 425.68 to Tenths (1 decimal place), Hundredths (2 decimal place) and to Tens place?

a) 425.6, 425.68, 426

b) 425.7, 425.68, 430

c) 425.5, 426.78, 425

d) 425.7, 4257, 430

View Answer

Explanation: In the Tenths (1 decimal place), we will take 68 as a digit after the decimal and round off it to the multiple of ten as 70, In the hundredths (2 decimal place), we will take both 68 as a number after the decimal because we have to take 2 decimal places and 6,8 both numbers are greater than 5, In the Tens place, we will round the number before the decimal place to the closest multiple of ten, i.e. 430.

3. A piece of iron rod was measured and found to be 120cms. But the actual value of the wood is 123cms. Find the relative error?

a) 3%

b) 2.5%

c) 2.43%

d) 3.43%

View Answer

Explanation: Given:

True value = 123cms

Measured value = 120cms

Firstly, let us find out the absolute error.

We know by subtracting true value with measured value we get absolute error = 123 – 120 = 3cms

Therefore, absolute error = 3cms

Now, let us find out the relative error = absolute error/True value x 100

= 3/123 x 100 = 2.43%

Therefore, the relative error for the given values = 2.43%.

4. Which of the following is correct according to calculating relative error as a measure of Precision?

a) (Absolute error/ True value)*100

b) (Absolute error/True value)

c) (measurement being taken/Absolute error)*100

d) (Absolute error/measurement being taken)

View Answer

Explanation: Relative error (RE) — when used as a measure of precision — is the ratio of the absolute error of a measurement to the measurement being taken. In other words, this type of error is relative to the size of the item being measured. RE is expressed as a percentage and has no units.

5. From the below data which one is precise?

Sample A: 15.38, 15.37, 15.36, 15.33, and 15.32. Sample B: 32.56, 32.55, 32.48, 32.49 and 32.48.

a) Sample A

b) Sample B

c) Sample A & B

d) None of the mentioned

View Answer

Explanation: Subtract the lowest data point from the highest:

Sample A: 15.38 – 15.32 = 0.06

Sample B: 32.56 – 32.48 = 0.08

Sample A has the lowest range (.06) and so is the more precise.

6. If a student measured the mass of an object on a balance three times and obtained the values 14.568 g, 14.566 g, and 14.565 g, the range and percent of the average value between the measurements would be ____________

a) 0.005gm, 0.01%

b) 0.004gm,0.02%

c) 0.003gm,0.02%

d) 0.001gm,0.01%

View Answer

Explanation: Range = (14.568 – 14.565) g = 0.003 g,

This is a reasonable range; the uncertainty appears in the last significant figure of the measured value, as it should.

The average value for the mass of the object is 14.566 g. Therefore:

% of average = (0.003 g/14.566 g) x 100% = 0.02%

the range as a percent of average (RPA) has only one significant figure in this case because the numerator of the fraction has only one.

7. The accepted value for the density of gold metal is 19.31 g/cm^{3}. If a student measured the mass and volume of a sample of gold, and obtained a value of 19.03 g/cm^{3}, the percent difference would be ______

a) -1.5%

b) 1.5%

c) -0.5%

d) 0.5%

View Answer

Explanation: % difference = [(19.03 – 19.31) g/19.31 g] x 100% = – 1.5%

A percent difference can be positive or negative; the sign shows whether the experimental value is higher or lower than the actual or theoretical value. This distinction is not used in precision since all values are experimental.

8. A group of students worked in separate teams to measure the length of an object. Here are their data: Find out:-

i) The average length

ii) The range or spread

iii) The precision of the measurement

a) 2.7, 0.2, 2.7±0.2

b) 2.8, 0.1, 2.8±0.1

c) 2.0, 0.1, 2.0±0.1

d) 2.0, 0.2, 2.0±0.2

View Answer

Explanation: The average length is the mean or average, in which the summation of the total number is divided from the total number, i.e.

(2.65+2.60+2.77+2.80+2.75)cm/5 = 13.57cm/5 = 2.714cm or 2.7cm

The range or spread is the subtraction from the highest value from the lowest value, i.e.,

Highest value = 2.80cm

Lowest value = 2.60cm

Therefore, Range = 2.80cm-2.60cm = 0.2cm

The precision of the measurement can be shown as average± range cm, i.e.,

Average = 2.7cm

Range = 0.2cm

Therefore, Precision = 2.7±0.2cm.

9. You are given a cube of pure copper. You measure the sides of the cube to find the volume and weigh it to find its mass. When you calculate the density using your measurements, you get 8.78 grams/cm^{3}. Coppers accepted density is 8.96 g/cm^{3}. What is your percent error?

a) 1%

b) 0.02%

c) 0.01%

d) 2%

View Answer

Explanation: Experimental value = 8.78 g/cm

^{3}

Accepted value = 8.96 g/cm

^{3}

Step 1: Subtract the accepted value from the experimental value.

8.78 g/cm

^{3}– 8.96 g/cm

^{3}= -0.18 g/cm

^{3}

Step 2: Take the absolute value of step 1

|-0.18 g/cm

^{3}| = 0.18 g/cm

^{3}

Step 3: Divide that answer by the accepted value, 0.18g/cm

^{3}÷ 8.96g/cm

^{3}= 0.02

Step 4: Multiply that answer by 100 and add the % symbol to express the answer as a percentage.

0.02 x 100 = 2

The percent error of your density calculation was 2%.

10. What type of surface you would observe in the case of mercury with glass?

a) Concave meniscus

b) Convex meniscus

c) Contact angle = 180°

d) Contact angle = 0°

View Answer

Explanation: A convex meniscus occurs when the molecules have a stronger attraction to each other than to the container and Mercury does not wet glass – the cohesive forces within the drops i.e., bond between the molecules of mercury are stronger than the adhesive forces between the drops and glass.

11. You will read the meniscus reading as you measure the level at the horizontal center or inside part of the meniscus.

a) True

b) False

View Answer

Explanation: Place the graduated cylinder on a flat surface and view the height of the liquid in the cylinder with your eyes directly level with the liquid. The liquid will tend to curve downward. This curve is called the meniscus. Always read the measurement at the bottom of the meniscus.

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