Question 1

Light travels at 3 $\times$ 10⁸ m/s, and the size of a proton is about 1 fm. Calculate the order of magnitude for the time taken for light to pass across a proton. A) 10^-7 s B) 10^-8 s C) 10^-22 s D) 10^-23 s E) 10²³ s

Accepted Answer

The answer of Light travels at 3 $\times$ 10⁸ m/s,...

Question 2

The mass of an electron is of the order of 10^-30 kg and the mass of the universe is believed to be of the order of 10⁵² kg. From this information you can conclude that A) the mass of Earth is 52 orders of magnitude greater than that of the electron. B) the mass of Earth is 30 orders of magnitude greater than that of the electron. C) the mass of the electron is 82 orders of magnitude greater than that of Earth. D) the mass of Earth is 82 orders of magnitude greater than that of the electron. E) the mass of the electron is 30 orders of magnitude greater than that of Earth.

Accepted Answer

The difference in orders of magnitude between the mass of the electron and the mass of the universe is 152, which means the mass of the universe is 152 orders of magnitude greater than that of the electron. Therefore, the difference in orders of magnitude between the mass of the electron and the mass of Earth would be 152 - 30 = 122. This means that the mass of Earth is 122 orders of magnitude greater than that of the electron, which can be rounded to 82 orders of magnitude (since the option 82 orders of magnitude is closer to the actual value than option 122). Hence, choice D is correct.

Question 3

The momentum of a body is defined to be the product of its mass and its velocity. If the mass of an air-track glider is known to be 225 g and its velocity is measured to be 3.1 cm/s, its momentum should be reported as A) 697.5 g · cm/s B) 698 g · cm/s C) 7.0 $\times$ 10² g · cm/s D) 6.98 $\times$ 10² g · cm/s E) 6.975 $\times$ 10² g · cm/s

Accepted Answer

The answer of The momentum of a body is defined...

Question 4

What is the order of magnitude of Earth's tallest mountain heights? A) 10⁸ m B) 10⁴ m C) 10⁶ m D) 10³ m E) 10⁵ m

Accepted Answer

The answer of What is the order of magnitude of...

Question 5

Estimate the number of raindrops needed to fill a volume of 1m $\times$ 1m $\times$ 1cm. A) 10³ B) 10⁵ C) 10⁷ D) 10⁹ E) 10¹¹

Accepted Answer

The volume of the given space is 1m x 1m x 1cm = 0.01 m^3.
Assuming each raindrop is a sphere with a radius of 1mm (0.001m), the volume of each raindrop can be calculated using the formula for the volume of a sphere, V = (4/3)πr^3, where V is the volume and r is the radius.
V = (4/3)π(0.001)^3 ≈ 4.188 x 10^-9 m^3.
The number of raindrops needed can be calculated by dividing the total volume by the volume of one raindrop.
Number of raindrops = 0.01/4.188 x 10^-9 ≈ 2.39 x 10^6.
This number is closest to the answer in option C, 10^17.

Question 6

The chemical agent dioxin can be toxic or hazardous to humans in concentrations as small as one part per billion. If I am testing a soil sample that has a mass of 1.0 kg, how much dioxin would have to be present for me to label it toxic or hazardous?
A) a picogram
B) a kilogram
C) a microgram
D) a milligram
E) a nanogram

Accepted Answer

The answer of The chemical agent dioxin can be toxic...

Question 7

If Earth is approximately 4.5 billion years old, estimate the order of magnitude for the number of times it has rotated about its own axis. (Assume a constant rate of rotation.) A) 10⁹ B) 10¹⁰ C) 10¹¹ D) 10¹² E) 10¹⁴

Accepted Answer

Given that Earth is approximately 4.5 billion years old and assuming a constant rate of rotation with about 365.25 days per year, we can estimate the number of rotations (days) as follows: 4.5 billion years * 365.25 days/year = 1.64 * 10^9 * 365.25 ≈ 6 * 10^11. This calculation puts the order of magnitude for the number of times Earth has rotated about its own axis at 10^12, which corresponds to choice D (10^12).

Question 8

An impurity in a manufacturing process will cause a batch to be rejected if the impurity exceeds one part per million. What is the maximum amount of impurity that could be present if the batch contains 100 kg of the product?
A) 100 micrograms
B) 100 nanograms
C) 100 grams
D) 100 megagrams
E) 100 milligrams

Accepted Answer

The maximum amount of impurity that could be present in one part per million (ppm) in 100 kg of product can be calculated as:
1 ppm = (1/1,000,000) * 100 kg = 0.1 g = 100 mg. Therefore, the maximum amount of impurity that could be present is 100 milligrams.

Question 9

The size of a proton is of the order of 10^-15 m and the size of the visible universe is of the order of 10²⁶ m. From this information you can conclude that A) the size of the universe is 26 orders of magnitude greater than that of the proton. B) the size of the universe is 41 orders of magnitude greater than that of the proton. C) the size of the proton is 11 orders of magnitude greater than that of the universe. D) the size of the universe is 15 orders of magnitude greater than that of the proton. E) the size of the proton is 15 orders of magnitude greater than that of the universe.

Accepted Answer

The difference between the sizes of the proton and the universe is given by the exponent of the scientific notation. Therefore, the difference is 126-(-15) = 141. Therefore, the size of the universe is 141 orders of magnitude greater than that of the proton, which corresponds to option B.

Question 10

The net force acting on a body is defined to be the product of the mass of the body and its resultant acceleration. If the mass of a body is known to be 184 kg and its acceleration is measured to be 2.4 m/s², the resultant force should be reported as A) 4.4 $\times$ 10² kg · m/s² B) 441.6 kg · m/s² C) 442 kg · m/s² D) 4.416 kg · m/s² E) 4.42 $\times$ 10² kg · m/s²

Accepted Answer

The answer of The net force acting on a body...

Question 11

Earth's population, expressed as an order of magnitude, is closest to A) 10⁶ B) 10¹⁰ C) 10⁵ D) 10⁸ E) 10⁷

Accepted Answer

The answer of Earth's population, expressed as an order of...

Question 12

Light travels at 3 $\times$10⁸ m/s, and it takes about 8 min for light from the sun to travel to Earth. Based on this, the order of magnitude of the distance from the sun to Earth is A) 10¹⁰ m B) 10⁸ m C) 10⁹ m D) 10⁶ m E) 10¹¹ m

Accepted Answer

The answer of Light travels at 3 $\times$10⁸ m/s, and...

Question 13

Compute: (12 $\times$ 10⁶ - 2 $\times$ 10⁷) / (-12 $\times$ 10⁷ + 7 $\times$10⁶) A) 7.1 $\times$ 10^-2 B) 7.0 $\times$ 10⁶ C) 2.0 $\times$ 10^-8 D) -7.1 $\times$10^-2 E) 2 $\times$10⁵

Accepted Answer

The answer of Compute: (12 $\times$ 10⁶ - 2 $\times$ 10⁷)...

Question 14

The measurement 5.130 $\times$10^-4 has _____ significant figures. A) two B) three C) one D) seven E) four

Accepted Answer

There are four non-zero digits in the measurement, therefore there are four significant figures. The zeros before the first non-zero digit and after the last non-zero digit are not significant. The zeros between the non-zero digits are significant.

Question 15

Which of the following represents a value of current measured to at least five significant figures? A) 2.375 $\times$ 10⁴ A B) 0.00347 A C) 3.0 $\times$ 10⁵ A D) 23.75 $\times$ 10¹ A E) 50.300 A

Accepted Answer

The answer of Which of the following represents a value...

Question 16

The measurement 23.0040 has _____ significant figures.
A) six
B) three
C) five
D) four
E) two

Accepted Answer

The measurement 23.0040 has six significant figures because all non-zero digits and zeros between significant figures are counted, including trailing zeros after the decimal point.

Question 17

A person inhales about 1 L of air per breathe. Estimate the number of air molecules inhaled. A) 10¹⁰ B) 10¹⁴ C) 10¹⁸ D) 10²² E) 10²⁶

Accepted Answer

The answer of A person inhales about 1 L of...

Question 18

The longest bridge on Earth is of the order of A) 10³ m B) 10⁴ m C) 10⁵ m D) 10⁶ m E) 10⁷m

Accepted Answer

The answer of The longest bridge on Earth is of...

Question 19

If you have a music CD collection of about 150 discs, estimate the order of magnitude of the number of heartbeats you would have if you listened all the way through your collection. A) 10⁶ B) 10⁸ C) 10¹⁰ D) 10⁴ E) 10³

Accepted Answer

The answer of If you have a music CD collection...

Question 20

The number of seconds in a month is of the order of A) 10³ B) 10⁸ C) 10⁵ D) 10¹⁰ E) 10⁶

Accepted Answer

The answer of The number of seconds in a month...

Quiz 1: Systems of Measurement

Light travels at 3 $\times$ 10⁸ m/s, and the size of a proton is about 1 fm. Calculate the order of magnitude for the time taken for light to pass across a proton.

The mass of an electron is of the order of 10^-30 kg and the mass of the universe is believed to be of the order of 10⁵² kg. From this information you can conclude that

The momentum of a body is defined to be the product of its mass and its velocity. If the mass of an air-track glider is known to be 225 g and its velocity is measured to be 3.1 cm/s, its momentum should be reported as

What is the order of magnitude of Earth's tallest mountain heights?

Estimate the number of raindrops needed to fill a volume of 1m $\times$ 1m $\times$ 1cm.

The chemical agent dioxin can be toxic or hazardous to humans in concentrations as small as one part per billion. If I am testing a soil sample that has a mass of 1.0 kg, how much dioxin would have to be present for me to label it toxic or hazardous?

If Earth is approximately 4.5 billion years old, estimate the order of magnitude for the number of times it has rotated about its own axis. (Assume a constant rate of rotation.)

An impurity in a manufacturing process will cause a batch to be rejected if the impurity exceeds one part per million. What is the maximum amount of impurity that could be present if the batch contains 100 kg of the product?

The size of a proton is of the order of 10^-15 m and the size of the visible universe is of the order of 10²⁶ m. From this information you can conclude that

The net force acting on a body is defined to be the product of the mass of the body and its resultant acceleration. If the mass of a body is known to be 184 kg and its acceleration is measured to be 2.4 m/s², the resultant force should be reported as

Earth's population, expressed as an order of magnitude, is closest to

Light travels at 3 $\times$ 10⁸ m/s, and it takes about 8 min for light from the sun to travel to Earth. Based on this, the order of magnitude of the distance from the sun to Earth is

Compute: (12 $\times$ 10⁶ - 2 $\times$ 10⁷) / (-12 $\times$ 10⁷ + 7 $\times$ 10⁶)

The measurement 5.130 $\times$ 10^-4 has _____ significant figures.

Which of the following represents a value of current measured to at least five significant figures?

The measurement 23.0040 has _____ significant figures.

A person inhales about 1 L of air per breathe. Estimate the number of air molecules inhaled.

The longest bridge on Earth is of the order of

If you have a music CD collection of about 150 discs, estimate the order of magnitude of the number of heartbeats you would have if you listened all the way through your collection.

The number of seconds in a month is of the order of