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
Show solution
Solution
Maximum possible voltage = Measured value + Uncertainty = 12.0 + 0.2 = 12.2 V.
Correct Answer: C — 12.2 V
Learn More →
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
Show solution
Solution
Fractional error = (absolute error / measured value) = 0.3 / 15.0 = 0.02.
Correct Answer: B — 0.03
Learn More →
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
Show solution
Solution
The absolute error is given directly as ±5 V.
Correct Answer: A — 5 V
Learn More →
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
Show solution
Solution
Relative error = Absolute error / Measured value = 10 / 1000 = 0.01.
Correct Answer: B — 0.1
Learn More →
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
Show solution
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
Learn More →
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%
Show solution
Solution
Relative error = (Absolute error / Measured value) * 100 = (5 / 200) * 100 = 2.5%
Correct Answer: A — 2.5%
Learn More →
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
Show solution
Solution
Absolute error = Relative error * True value = 0.1 * 10 = 1 kg.
Correct Answer: A — 1 kg
Learn More →
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%
Show solution
Solution
Percentage error = (Absolute error / Measured value) * 100 = (1 / 50) * 100 = 2%
Correct Answer: A — 2%
Learn More →
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
Show solution
Solution
Range of possible speeds = Measured speed ± Error = 60 ± 2 gives 58 to 62 km/h.
Correct Answer: A — 58 to 62 km/h
Learn More →
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
Show solution
Solution
The absolute error is given as 5 m.
Correct Answer: A — 5 m
Learn More →
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
Show solution
Solution
Maximum possible error is equal to the uncertainty, which is ±0.2 cm.
Correct Answer: B — 0.2 cm
Learn More →
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
Show solution
Solution
Minimum possible mass = Measured value - Error = 75 - 0.5 = 74.5 kg
Correct Answer: A — 74.5 kg
Learn More →
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
Show solution
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
Learn More →
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
Show solution
Solution
Maximum possible temperature = Measured value + Error = 25 + 0.5 = 25.5°C.
Correct Answer: A — 25.5°C
Learn More →
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
Show solution
Solution
Minimum temperature = Recorded temperature - Error = 25 - 0.5 = 24.5°C.
Correct Answer: A — 24.5°C
Learn More →
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
Show solution
Solution
Maximum possible temperature = Measured value + Error = 100 + 0.5 = 100.5°C.
Correct Answer: A — 100.5°C
Learn More →
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
Show solution
Solution
Range of possible volumes = 200 - 5 to 200 + 5 = 195 L to 205 L.
Correct Answer: A — 195 L to 205 L
Learn More →
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
Show solution
Solution
Maximum true weight = Measured weight + Error = 10 kg + 0.2 kg = 10.2 kg.
Correct Answer: A — 10.2 kg
Learn More →
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
Show solution
Solution
Relative error = (absolute error / measured value) = 0.5 / 30 = 0.0167.
Correct Answer: A — 0.0167
Learn More →
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
Show solution
Solution
Uncertainty in area = 2 * length * uncertainty in length = 2 * 10 * 0.1 = 2 m².
Correct Answer: B — 0.5 m²
Learn More →
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
Show solution
Solution
Circumference = 2πr. Measured circumference = 31.4 cm. Thus, r = 31.4 / (2π) ≈ 5.0 cm.
Correct Answer: C — 5.0 cm
Learn More →
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%
Show solution
Solution
Percentage error = (Absolute error / Measured value) * 100 = (0.2 / 31.4) * 100 ≈ 0.64%.
Correct Answer: A — 0.64%
Learn More →
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
Show solution
Solution
Relative uncertainty = (absolute uncertainty / density) = 0.2 / 8.0 = 0.025.
Correct Answer: B — 0.02
Learn More →
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
Show solution
Solution
The absolute error is given directly as ±0.1 g/cm³.
Correct Answer: A — 0.1 g/cm³
Learn More →
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
Show solution
Solution
Relative uncertainty = (absolute uncertainty / measured value) = 0.2 / 8.0 = 0.025.
Correct Answer: B — 0.02
Learn More →
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
Show solution
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
Learn More →
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
Show solution
Solution
Relative uncertainty = (absolute uncertainty / measured value) = 0.1 / 8.0 = 0.0125.
Correct Answer: B — 0.01
Learn More →
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
Show solution
Solution
Range = 8.0 ± 0.2 gives 7.8 to 8.2 g/cm³.
Correct Answer: A — 7.8 to 8.2 g/cm³
Learn More →
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
Show solution
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
Learn More →
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
Show solution
Solution
Fractional error = (absolute error / measured value) = 0.1 / 8.0 = 0.0125.
Correct Answer: B — 0.01
Learn More →
Showing 61 to 90 of 119 (4 Pages)
