Units & Measurement
Q. A voltage is measured as 12.0 V with an uncertainty of ±0.2 V. What is the maximum possible voltage?
A.
11.8 V
B.
12.0 V
C.
12.2 V
D.
12.4 V
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Solution
Maximum possible voltage = Measured value + Uncertainty = 12.0 + 0.2 = 12.2 V.
Correct Answer: C — 12.2 V
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Q. A voltage is measured as 15.0 V with an uncertainty of ±0.3 V. What is the fractional error in the voltage measurement?
A.
0.02
B.
0.03
C.
0.01
D.
0.05
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Solution
Fractional error = (absolute error / measured value) = 0.3 / 15.0 = 0.02.
Correct Answer: B — 0.03
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Q. A voltage measurement is taken as 220 V with an uncertainty of ±5 V. What is the absolute error?
A.
5 V
B.
10 V
C.
2.5 V
D.
0.5 V
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Solution
The absolute error is given directly as ±5 V.
Correct Answer: A — 5 V
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Q. A volume is measured as 1000 mL with an error of 10 mL. What is the relative error?
A.
0.01
B.
0.1
C.
0.001
D.
0.05
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Solution
Relative error = Absolute error / Measured value = 10 / 1000 = 0.01.
Correct Answer: B — 0.1
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Q. A volume is measured as 2.0 L with an uncertainty of ±0.1 L. If this volume is used to calculate density, what is the uncertainty in density if mass is measured as 4.0 kg with an uncertainty of ±0.2 kg?
A.
0.1 kg/L
B.
0.2 kg/L
C.
0.05 kg/L
D.
0.4 kg/L
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Solution
Using the formula for density (density = mass/volume), the uncertainty in density can be calculated using the formula for propagation of uncertainty.
Correct Answer: A — 0.1 kg/L
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Q. A volume is measured as 200 L with an error of 5 L. What is the relative error in percentage?
A.
2.5%
B.
5%
C.
1%
D.
0.5%
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Solution
Relative error = (Absolute error / Measured value) * 100 = (5 / 200) * 100 = 2.5%
Correct Answer: A — 2.5%
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Q. A weight is measured as 10 kg with a relative error of 0.1. What is the absolute error?
A.
1 kg
B.
0.1 kg
C.
0.5 kg
D.
0.2 kg
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Solution
Absolute error = Relative error * True value = 0.1 * 10 = 1 kg.
Correct Answer: A — 1 kg
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Q. A weight is measured to be 50 kg with a possible error of 1 kg. What is the percentage error in the measurement?
A.
2%
B.
1%
C.
0.5%
D.
5%
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Solution
Percentage error = (Absolute error / Measured value) * 100 = (1 / 50) * 100 = 2%
Correct Answer: A — 2%
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Q. Convert 5 kilometers to meters.
A.
500
B.
5000
C.
50
D.
5
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Solution
5 kilometers is equal to 5000 meters.
Correct Answer: B — 5000
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Q. How many centimeters are there in a meter?
A.
10
B.
100
C.
1000
D.
10000
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Solution
There are 100 centimeters in a meter.
Correct Answer: B — 100
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Q. How many millimeters are there in a meter?
A.
10
B.
100
C.
1000
D.
10000
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Solution
There are 1000 millimeters in a meter.
Correct Answer: C — 1000
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Q. How many seconds are there in an hour?
A.
60
B.
3600
C.
600
D.
120
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Solution
There are 3600 seconds in an hour (60 seconds x 60 minutes).
Correct Answer: B — 3600
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Q. How many significant figures are in the measurement 0.004560?
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Solution
The measurement 0.004560 has 4 significant figures (the leading zeros are not counted).
Correct Answer: B — 4
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Q. How many significant figures are in the measurement 0.05060?
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Solution
Leading zeros do not count, but the trailing zero after the decimal does. Therefore, 0.05060 has 4 significant figures.
Correct Answer: B — 4
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Q. How many significant figures are in the number 0.000500?
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Solution
The significant figures are 5, 0, and the trailing zero counts, totaling 3.
Correct Answer: B — 3
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Q. How many significant figures are in the number 0.004560?
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Solution
The number 0.004560 has 4 significant figures (the leading zeros are not counted).
Correct Answer: B — 4
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Q. How many significant figures are in the number 0.00456?
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Solution
Leading zeros do not count as significant figures. The significant figures in 0.00456 are 4, 5, and 6, which totals to 3 significant figures.
Correct Answer: B — 3
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Q. How many significant figures are in the number 0.007890?
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Solution
The significant figures are 7, 8, 9, and the trailing zero counts.
Correct Answer: C — 5
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Q. How many significant figures are in the number 100.0?
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Solution
The trailing zero after the decimal point counts as a significant figure.
Correct Answer: D — 4
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Q. How many significant figures are in the number 1002?
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Solution
All non-zero digits are significant, so 1002 has 4 significant figures.
Correct Answer: C — 4
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Q. How many significant figures are in the number 5000 when no decimal point is present?
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Solution
5000 has 1 significant figure unless specified otherwise (e.g., 5000. has 4 significant figures).
Correct Answer: A — 1
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Q. How many significant figures are in the number 5000?
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Solution
5000 has 1 significant figure unless specified with a decimal point (e.g., 5000. has 4).
Correct Answer: A — 1
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Q. How should the number 0.0001234 be rounded to two significant figures?
A.
0.00012
B.
0.00013
C.
0.0001
D.
0.000123
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Solution
To round 0.0001234 to two significant figures, we look at the first two non-zero digits (1 and 2) and round up, resulting in 0.00013.
Correct Answer: B — 0.00013
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Q. How should the number 0.05060 be rounded to three significant figures?
A.
0.051
B.
0.0506
C.
0.05060
D.
0.050
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Solution
To round 0.05060 to three significant figures, we keep the first three significant digits (5, 0, and 6), resulting in 0.0506.
Correct Answer: B — 0.0506
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Q. If a car travels 100 kilometers in 2 hours, what is its speed in meters per second?
A.
10 m/s
B.
20 m/s
C.
30 m/s
D.
40 m/s
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Solution
Speed = distance/time = (100000 m)/(7200 s) = 27.78 m/s, approximately 20 m/s.
Correct Answer: B — 20 m/s
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Q. If a car travels at a speed of 90 km/h, how far will it travel in 2 hours?
A.
90 km
B.
180 km
C.
200 km
D.
150 km
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Solution
At 90 km/h, the car will travel 180 km in 2 hours.
Correct Answer: B — 180 km
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Q. If a car's speed is measured as 60 km/h with an error of ±2 km/h, what is the range of possible speeds?
A.
58 to 62 km/h
B.
60 to 62 km/h
C.
58 to 64 km/h
D.
60 to 64 km/h
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Solution
Range of possible speeds = Measured speed ± Error = 60 ± 2 gives 58 to 62 km/h.
Correct Answer: A — 58 to 62 km/h
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Q. If a length is measured as 0.0500 m, how many significant figures does it have?
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Solution
Leading zeros are not significant. The significant figures are 5, 0, 0, which gives a total of 3 significant figures.
Correct Answer: C — 4
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Q. If a length is measured as 0.0600 m, how many significant figures does it have?
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Solution
The number 0.0600 m has 3 significant figures. The leading zeros do not count, but the trailing zeros after the decimal point do.
Correct Answer: C — 4
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Q. If a length is measured as 150.0 cm, how many significant figures does it have?
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Solution
The number 150.0 has 4 significant figures because the trailing zero after the decimal point counts as significant.
Correct Answer: C — 4
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