Units & Measurement
Q. What is the conversion factor from kilometers to meters?
A.
100
B.
1000
C.
0.1
D.
0.001
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Solution
The conversion factor from kilometers to meters is 1000, as 1 kilometer equals 1000 meters.
Correct Answer: B — 1000
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Q. What is the conversion factor from kilometers to miles?
A.
0.621
B.
1.609
C.
0.539
D.
1.000
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Solution
1 kilometer is approximately equal to 0.621 miles.
Correct Answer: B — 1.609
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Q. What is the correct number of significant figures in the result of 5.67 - 0.2?
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Solution
The result should be rounded to 3 significant figures, giving 5.5.
Correct Answer: B — 3
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Q. What is the correct number of significant figures in the result of 6.022 x 10^23?
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Solution
6.022 has 4 significant figures, so the result retains that count.
Correct Answer: D — 5
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Q. What is the correct way to express 0.000123 in scientific notation with significant figures?
A.
1.23 x 10^-4
B.
1.23 x 10^-3
C.
1.2 x 10^-4
D.
1.23 x 10^-5
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Solution
In scientific notation, 0.000123 is expressed as 1.23 x 10^-4, maintaining 3 significant figures.
Correct Answer: A — 1.23 x 10^-4
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Q. What is the correct way to express 0.000123 in scientific notation?
A.
1.23 x 10^-4
B.
1.23 x 10^-3
C.
1.23 x 10^-2
D.
1.23 x 10^-5
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Solution
In scientific notation, 0.000123 is expressed as 1.23 x 10^-4.
Correct Answer: A — 1.23 x 10^-4
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Q. What is the correct way to express 0.0001234 in scientific notation with significant figures?
A.
1.234 x 10^-4
B.
1.23 x 10^-4
C.
1.2340 x 10^-4
D.
1.2 x 10^-4
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Solution
In scientific notation, all non-zero digits are significant. Therefore, 0.0001234 can be expressed as 1.234 x 10^-4, maintaining all significant figures.
Correct Answer: A — 1.234 x 10^-4
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Q. What is the correct way to express 0.000345 in scientific notation with significant figures?
A.
3.45 x 10^-4
B.
3.450 x 10^-4
C.
3.4500 x 10^-4
D.
3.4 x 10^-4
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Solution
In scientific notation, all digits in the coefficient are significant. Therefore, 0.000345 is expressed as 3.45 x 10^-4, which has 3 significant figures.
Correct Answer: A — 3.45 x 10^-4
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Q. What is the correct way to express 0.000450 in scientific notation with significant figures?
A.
4.5 x 10^-4
B.
4.50 x 10^-4
C.
0.45 x 10^-3
D.
4.500 x 10^-4
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Solution
In scientific notation, 0.000450 is expressed as 4.50 x 10^-4, maintaining three significant figures.
Correct Answer: B — 4.50 x 10^-4
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Q. What is the dimension of electric charge?
A.
[M^1 L^2 T^-3 I^1]
B.
[M^0 L^0 T^0 I^1]
C.
[M^1 L^1 T^-2 I^1]
D.
[M^0 L^1 T^-1 I^1]
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Solution
The dimension of electric charge is [M^1 L^2 T^-3 I^1].
Correct Answer: A — [M^1 L^2 T^-3 I^1]
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Q. What is the dimension of frequency?
A.
M^0L^0T^-1
B.
M^1L^0T^-1
C.
M^0L^1T^-1
D.
M^0L^0T^0
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Solution
Frequency is defined as the number of cycles per unit time, thus its dimension is [M^0L^0T^-1].
Correct Answer: A — M^0L^0T^-1
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Q. What is the dimension of the gravitational constant G?
A.
M^-1L^3T^-2
B.
M^1L^3T^-2
C.
M^1L^2T^-2
D.
M^0L^0T^0
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Solution
The gravitational constant G has dimensions of [M^-1L^3T^-2] as it relates mass, distance, and time in the law of gravitation.
Correct Answer: A — M^-1L^3T^-2
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Q. What is the dimensional formula for acceleration?
A.
[M^0 L^1 T^-2]
B.
[M^0 L^0 T^-2]
C.
[M^1 L^1 T^-2]
D.
[M^1 L^0 T^-2]
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Solution
The dimensional formula for acceleration is [M^0 L^1 T^-2], as it is defined as the change in velocity per unit time.
Correct Answer: A — [M^0 L^1 T^-2]
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Q. What is the dimensional formula for electric charge?
A.
[M^1 L^2 T^-3 I^-1]
B.
[M^0 L^0 T^1 I^1]
C.
[M^0 L^1 T^-2 I^1]
D.
[M^1 L^1 T^-2 I^-1]
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Solution
The dimensional formula for electric charge is [M^1 L^2 T^-3 I^-1], derived from the definition of current (I = Q/t).
Correct Answer: A — [M^1 L^2 T^-3 I^-1]
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Q. What is the dimensional formula for energy?
A.
[M^1 L^2 T^-2]
B.
[M^1 L^1 T^-2]
C.
[M^1 L^2 T^0]
D.
[M^0 L^1 T^-2]
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Solution
Energy has the dimensional formula [M^1 L^2 T^-2], as it is measured in Joules (1 J = 1 kg·m²/s²).
Correct Answer: A — [M^1 L^2 T^-2]
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Q. What is the dimensional formula for frequency?
A.
[M^0 L^0 T^-1]
B.
[M^1 L^0 T^-1]
C.
[M^0 L^1 T^0]
D.
[M^0 L^0 T^1]
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Solution
The dimensional formula for frequency is [M^0 L^0 T^-1], as it is defined as the number of cycles per unit time.
Correct Answer: A — [M^0 L^0 T^-1]
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Q. What is the dimensional formula for pressure?
A.
M¹L⁻¹T⁻²
B.
M¹L²T⁻²
C.
M⁰L⁰T⁰
D.
M¹L⁰T⁻²
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Solution
Pressure is defined as force per unit area. The dimensional formula for force is M¹L¹T⁻², and for area is L², thus pressure = M¹L¹T⁻² / L² = M¹L⁻¹T⁻².
Correct Answer: A — M¹L⁻¹T⁻²
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Q. What is the dimensional formula for velocity?
A.
MLT⁻¹
B.
ML²T⁻²
C.
M⁰L⁰T⁻¹
D.
M⁰L¹T⁻²
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Solution
Velocity is defined as displacement per unit time, which gives the dimensional formula of [MLT⁻¹].
Correct Answer: A — MLT⁻¹
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Q. What is the dimensional formula for work?
A.
[M^1 L^2 T^-2]
B.
[M^1 L^1 T^-1]
C.
[M^0 L^2 T^-2]
D.
[M^1 L^0 T^-2]
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Solution
Work has the dimensional formula [M^1 L^2 T^-2].
Correct Answer: A — [M^1 L^2 T^-2]
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Q. What is the equivalent of 1 liter in cubic meters?
A.
0.001 m³
B.
0.01 m³
C.
0.1 m³
D.
1 m³
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Solution
1 liter is equal to 0.001 cubic meters.
Correct Answer: A — 0.001 m³
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Q. What is the number of significant figures in 0.0001230?
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Solution
The significant figures are 1, 2, 3, and the trailing zero counts.
Correct Answer: C — 5
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Q. What is the number of significant figures in the measurement 0.00456?
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Solution
The significant figures are 4, 5, and 6. Leading zeros are not counted.
Correct Answer: B — 3
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Q. What is the prefix for 10^-6 in the SI system?
A.
Milli
B.
Micro
C.
Nano
D.
Pico
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Solution
The prefix for 10^-6 is 'Micro'.
Correct Answer: B — Micro
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Q. What is the product of 3.00 and 2.5, considering significant figures?
A.
7.5
B.
7.50
C.
7.500
D.
7.55
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Solution
In multiplication, the result should have the same number of significant figures as the factor with the least significant figures. 3.00 has 3 significant figures and 2.5 has 2 significant figures, so the result should have 2 significant figures: 7.5.
Correct Answer: A — 7.5
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Q. What is the relationship between Celsius and Kelvin?
A.
K = C + 273.15
B.
K = C - 273.15
C.
C = K + 273.15
D.
C = K - 273.15
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Solution
The relationship is K = C + 273.15, where K is the temperature in Kelvin and C is the temperature in Celsius.
Correct Answer: A — K = C + 273.15
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Q. What is the relationship between Joules and Newton-meters?
A.
They are equal
B.
Joule is greater
C.
Newton-meter is greater
D.
They are unrelated
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Solution
1 Joule is defined as 1 Newton-meter, so they are equal.
Correct Answer: A — They are equal
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Q. What is the relationship between mass and weight?
A.
Weight = Mass × Acceleration due to gravity
B.
Weight = Mass / Acceleration due to gravity
C.
Weight = Mass + Acceleration due to gravity
D.
Weight = Mass - Acceleration due to gravity
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Solution
Weight is defined as the force due to gravity acting on a mass, given by the formula Weight = Mass × g (where g is the acceleration due to gravity).
Correct Answer: A — Weight = Mass × Acceleration due to gravity
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Q. What is the relationship between the Celsius and Kelvin scales?
A.
K = C + 273.15
B.
C = K + 273.15
C.
K = C - 273.15
D.
C = K - 273.15
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Solution
The relationship is K = C + 273.15, where K is the temperature in Kelvin and C is the temperature in Celsius.
Correct Answer: A — K = C + 273.15
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Q. What is the relationship between the units of energy and work?
A.
They are the same
B.
Energy is greater than work
C.
Work is greater than energy
D.
They are different
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Solution
Energy and work are measured in the same unit, which is Joules (J).
Correct Answer: A — They are the same
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Q. What is the relationship between the units of work and energy?
A.
They are the same
B.
Work is a subset of energy
C.
Energy is a subset of work
D.
They are unrelated
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Solution
Work and energy are measured in the same unit, which is Joules (J) in the SI system.
Correct Answer: A — They are the same
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