Question 1

The measurement 23.0040 has _____ significant figures.

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 2

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

Accepted Answer

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

Question 3

The longest bridge on Earth is of the order of

Accepted Answer

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

Question 4

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

Accepted Answer

The difference between the size of the proton and the size of the universe is given by:
10^26 - 10^-15
Simplifying this expression gives:
10^41
Therefore, the size of the universe is 41 orders of magnitude greater than that of the proton.

Question 5

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?

Accepted Answer

A concentration of one part per billion (ppb) in a 1.0 kg soil sample corresponds to 1 microgram of dioxin.

Question 6

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

Accepted Answer

(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1F1F10 2 F1F1F1S1F1F1F10 10⁷)/ (F1F1F1S1F1F1F1012 F1F1F1S1F1F1F10 10⁷ + 7 F1F1F1S1F1F1F10 10⁶)=(12 F1F1F1S1F1F1F10 10⁶ F1F1F1S1F1

Question 7

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

Accepted Answer

The Earth's population is approximately 8 billion, which is closest to 10^10 when expressed as an order of magnitude.

Question 8

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

Accepted Answer

The distance is calculated by multiplying the speed of light (3 x 10^8 m/s) by the time it takes for light to travel from the sun to Earth (8 minutes or 480 seconds), resulting in approximately 1.44 x 10^11 meters, which is of the order of magnitude 10^11 m.

Question 9

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

Accepted Answer

A month typically has about 30 days, and each day has 86,400 seconds (24 hours x 60 minutes x 60 seconds). Therefore, the number of seconds in a month is approximately 2,592,000, which is of the order of 10^6.

Question 10

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

Accepted Answer

The significant figures in a measurement are determined by the number of digits that are reliable and certain, plus one estimated digit. In this case, all the digits before the decimal point are reliable and certain, so they all count as significant figures. The zero after the decimal point is also a significant figure because it indicates that the measurement was made to the nearest 0.1 unit. Therefore, there are four significant figures in this measurement: 5.130.

Question 11

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

Accepted Answer

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

Question 12

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

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 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

The correct answer is E because it is the only choice that has five significant figures.

Question 15

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

Accepted Answer

Volume of 1 cm = 0.000001 m^3
Volume of a raindrop (assumed spherical) = (4/3) * π * r^3, where r is approximately 0.002 m (2 mm)
Using these values, we can estimate the number of raindrops needed to fill the volume of 1 cm:
(0.000001 m^3) / [(4/3) * π * (0.002 m)^3] = 655.13
Rounding up, we get approximately 656 raindrops.
The only answer choice that comes close to this is C, which has 10^17 raindrops (i.e. 10 followed by 17 zeroes). This is a reasonable estimate, considering that 1 m x 1 m x 1 cm is a relatively small volume compared to the vast expanse of the atmosphere from which rain falls.

Question 16

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.

Accepted Answer

The average CD has about 70 minutes of music. If you listen to all 150 CDs, that's about 10,500 minutes of music. If your heart beats about 70 times per minute, that's about 735,000 heartbeats. The order of magnitude of this number is 10^6.

Question 17

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.)

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 18

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?

Accepted Answer

One part per million (ppm) means one unit of impurity per million units of product. For a 100 kg batch, 1 ppm is 100 milligrams.

Question 19

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

Accepted Answer

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

Question 20

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.

Accepted Answer

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

Quiz 1: Systems of Measurement

The measurement 23.0040 has _____ significant figures.

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

The longest bridge on Earth is of the order of

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 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?

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

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

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

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

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

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

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

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

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.

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 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

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.

Quiz 1: Systems of Measurement

The measurement 23.0040 has _____ significant figures.

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

The longest bridge on Earth is of the order of

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 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?

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

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

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

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

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

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

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

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

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.

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 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

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 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

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

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

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

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

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

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

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.