Error Analysis
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. 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 250 m with an error of 5 m, what is the absolute error?
A.
5 m
B.
0.5 m
C.
0.05 m
D.
50 m
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Solution
The absolute error is given as 5 m.
Correct Answer: A — 5 m
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Q. If a length is measured as 30.0 cm with an uncertainty of ±0.2 cm, what is the maximum possible error?
A.
0.1 cm
B.
0.2 cm
C.
0.3 cm
D.
0.4 cm
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Solution
Maximum possible error is equal to the uncertainty, which is ±0.2 cm.
Correct Answer: B — 0.2 cm
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Q. If a mass is measured as 75 kg with an error of 0.5 kg, what is the minimum possible mass?
A.
74.5 kg
B.
75 kg
C.
75.5 kg
D.
76 kg
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Solution
Minimum possible mass = Measured value - Error = 75 - 0.5 = 74.5 kg
Correct Answer: A — 74.5 kg
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Q. If a measurement of time is recorded as 15.0 s with an uncertainty of ±0.5 s, what is the total time range?
A.
14.5 s to 15.5 s
B.
15.0 s to 16.0 s
C.
14.0 s to 15.0 s
D.
15.0 s to 15.5 s
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Solution
Total time range = 15.0 ± 0.5 = 14.5 s to 15.5 s.
Correct Answer: A — 14.5 s to 15.5 s
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Q. If a temperature is recorded as 25°C with an error of ±0.5°C, what is the maximum possible temperature?
A.
25.5°C
B.
24.5°C
C.
26°C
D.
25°C
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Solution
Maximum possible temperature = Measured value + Error = 25 + 0.5 = 25.5°C.
Correct Answer: A — 25.5°C
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Q. If a temperature is recorded as 25°C with an error of ±0.5°C, what is the minimum temperature?
A.
24.5°C
B.
25°C
C.
25.5°C
D.
26°C
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Solution
Minimum temperature = Recorded temperature - Error = 25 - 0.5 = 24.5°C.
Correct Answer: A — 24.5°C
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Q. If a thermometer reads 100°C with an error of ±0.5°C, what is the maximum possible temperature?
A.
100.5°C
B.
99.5°C
C.
101°C
D.
100°C
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Solution
Maximum possible temperature = Measured value + Error = 100 + 0.5 = 100.5°C.
Correct Answer: A — 100.5°C
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Q. If a volume is measured as 200 L with an error of 5 L, what is the range of possible volumes?
A.
195 L to 205 L
B.
200 L to 205 L
C.
195 L to 210 L
D.
200 L to 210 L
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Solution
Range of possible volumes = 200 - 5 to 200 + 5 = 195 L to 205 L.
Correct Answer: A — 195 L to 205 L
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Q. If a weight is measured as 10 kg with a 0.2 kg error, what is the maximum possible true weight?
A.
10.2 kg
B.
9.8 kg
C.
10 kg
D.
10.4 kg
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Solution
Maximum true weight = Measured weight + Error = 10 kg + 0.2 kg = 10.2 kg.
Correct Answer: A — 10.2 kg
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Q. If the area of a rectangle is calculated as 30 m² with an uncertainty of ±0.5 m², what is the relative error in the area measurement?
A.
0.0167
B.
0.017
C.
0.015
D.
0.02
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Solution
Relative error = (absolute error / measured value) = 0.5 / 30 = 0.0167.
Correct Answer: A — 0.0167
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Q. If the area of a rectangle is calculated as 50 m² with a length of 10 m and an uncertainty of ±0.1 m in length, what is the uncertainty in the area?
A.
1 m²
B.
0.5 m²
C.
0.2 m²
D.
0.1 m²
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Solution
Uncertainty in area = 2 * length * uncertainty in length = 2 * 10 * 0.1 = 2 m².
Correct Answer: B — 0.5 m²
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Q. If the circumference of a circle is measured as 31.4 cm with an error of 0.2 cm, what is the radius?
A.
5 cm
B.
4.5 cm
C.
5.0 cm
D.
6 cm
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Solution
Circumference = 2πr. Measured circumference = 31.4 cm. Thus, r = 31.4 / (2π) ≈ 5.0 cm.
Correct Answer: C — 5.0 cm
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Q. If the circumference of a circle is measured as 31.4 cm with an error of 0.2 cm, what is the percentage error?
A.
0.64%
B.
0.5%
C.
1%
D.
0.2%
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Solution
Percentage error = (Absolute error / Measured value) * 100 = (0.2 / 31.4) * 100 ≈ 0.64%.
Correct Answer: A — 0.64%
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Q. If the density of a substance is calculated as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the relative uncertainty?
A.
0.025
B.
0.02
C.
0.005
D.
0.01
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Solution
Relative uncertainty = (absolute uncertainty / density) = 0.2 / 8.0 = 0.025.
Correct Answer: B — 0.02
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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.5 g/cm³, what is the range of possible values for the density?
A.
7.5 to 8.5 g/cm³
B.
8.0 to 8.5 g/cm³
C.
8.0 to 9.0 g/cm³
D.
7.0 to 9.0 g/cm³
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Solution
Range = (8.0 - 0.5) to (8.0 + 0.5) = 7.5 to 8.5 g/cm³.
Correct Answer: A — 7.5 to 8.5 g/cm³
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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³, what is the relative uncertainty in the density?
A.
0.0125
B.
0.01
C.
0.005
D.
0.02
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Solution
Relative uncertainty = (absolute uncertainty / measured value) = 0.1 / 8.0 = 0.0125.
Correct Answer: B — 0.01
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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the range of possible densities?
A.
7.8 to 8.2 g/cm³
B.
7.5 to 8.5 g/cm³
C.
8.0 to 8.4 g/cm³
D.
8.0 to 8.2 g/cm³
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Solution
Range = 8.0 ± 0.2 gives 7.8 to 8.2 g/cm³.
Correct Answer: A — 7.8 to 8.2 g/cm³
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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the absolute error in the volume calculated from this density?
A.
0.025 cm³
B.
0.1 cm³
C.
0.2 cm³
D.
0.5 cm³
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Solution
Volume = mass/density; if mass is constant, the absolute error in volume = (mass * absolute error in density) / (density²).
Correct Answer: A — 0.025 cm³
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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³, what is the fractional error in the density?
A.
0.0125
B.
0.01
C.
0.005
D.
0.02
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Solution
Fractional error = (absolute error / measured value) = 0.1 / 8.0 = 0.0125.
Correct Answer: B — 0.01
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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³, what is the absolute error in the density?
A.
0.1 g/cm³
B.
0.01 g/cm³
C.
0.5 g/cm³
D.
0.2 g/cm³
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Solution
The absolute error is given directly as ±0.1 g/cm³.
Correct Answer: A — 0.1 g/cm³
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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the relative uncertainty in the density?
A.
0.025
B.
0.02
C.
0.005
D.
0.1
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Solution
Relative uncertainty = (absolute uncertainty / measured value) = 0.2 / 8.0 = 0.025.
Correct Answer: B — 0.02
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