Question 1

Assume when using a meter stick measuring can be done so that the last significant figure is in the tenth of a millimeter digit.If you are measuring an object with length between 8 and 9 cm,how many significant figures will result if you only use the part of the meter stick between the 82-cm and 93-cm positions?

Accepted Answer

The part of the meter stick between the 82-cm and 93-cm positions measures a length of 11 cm. Since the last significant figure is in the tenth of a millimeter digit, we need to convert 11 cm to millimeters and round to the tenths place. 
11 cm = 110 mm 
Rounding to the tenths place, we get 110.0 mm. 
Since the length of the object being measured falls between 8 and 9 cm, only the first digit (1) and second digit (0) are significant. Therefore, there are 2 significant figures in the measurement taken using the part of the meter stick between the 82-cm and 93-cm positions.

Question 2

Assume when using a meter stick measuring can be done so that the last significant figure is in the tenth of a millimeter digit.If you are measuring an object with length between 25 and 53 cm,how many significant figures will result if you only use the part of the meter stick between the 3-cm and 85-cm positions?

Accepted Answer

The answer of Assume when using a meter stick measuring...

Question 3

There are other ways of expressing uncertainty besides significant figures.For example,suppose a quantity is known to have a value between 20.4 and 20.0,and our best estimate of the value is midrange at 20.2.We could write the number as 20.2 +/− 0.2 and say that the number has a 1% uncertainty.We would also say it has 3 significant figures.If we square a number with 1% uncertainty and 3 significant figures,what results?

Accepted Answer

The answer of There are other ways of expressing uncertainty...

Question 4

Suppose an equation relating position,x,to time,t,is given by x = bt³ + ct⁴,where b and c are constants.The dimensions of b and c are respectively:

Accepted Answer

The dimensions of b and c must compensate for the time dimensions in the equation to result in a position (x) dimension, which is length (L). Thus, for $x = bt^3 + ct^4$, b has dimensions of $L/T^3$ and c has dimensions of $L/T^4$ to ensure the equation's dimensional consistency.

Question 5

Which one of the choices below represents the preferred practice regarding significant figures when multiplying the following: 15.0 × 5.6 × 2.33?

Accepted Answer

The answer of Which one of the choices below represents...

Question 6

When SI units are plugged into an equation,it is found that the units balance.Which of the following can we expect to be true for this equation?

Accepted Answer

If the units balance in an equation, it means that the left-hand side and the right-hand side have the same dimensions. This is known as dimensional analysis. If we use SI units, which are based on fundamental units such as meters, kilograms, and seconds, then the dimensions of each term in the equation can be expressed in terms of these fundamental units. If the units balance, then each term on the left-hand side has the same dimensions as each term on the right-hand side. This ensures that the equation is dimensionally correct. However, it does not guarantee that all the constants of proportionality in the equation are correct.

Question 7

​A rectangular-shaped patio has a base length equal to (24.5 ± 0.2)m and a height equal to (9.3 ± 0.1)m.What is the area of the patio,including its uncertainty?

Accepted Answer

The area of the patio is calculated by multiplying the base length by the height, which gives 24.5m * 9.3m = 227.85m², rounded to 228m². The uncertainty in the area is found by adding the relative uncertainties of the length and height before multiplying by the area: (0.2/24.5 + 0.1/9.3) * 228 ≈ 4. Therefore, the area of the patio, including its uncertainty, is 228 ± 4 m².

Question 8

Calculate (0.83 + 0.049)(4.4 × 10³),keeping only significant figures.

Accepted Answer

The answer of Calculate (0.83 + 0.049)(4.4 × 10³),keeping only...

Question 9

A cement truck can pour 160 cubic yards of cement per hour.Express this in ft³/min.

Accepted Answer

The answer of A cement truck can pour 160 cubic...

Question 10

The length and width of a standard sheet of paper is measured,and then the area is found by calculation to be 91.50 in.².The number of significant figures in the width measurement must be at least

Accepted Answer

To find the area of the paper, we need to multiply the length by the width. Since the area has two decimal places, we want to make sure that the width measurement has at least two significant figures. Therefore, we need to choose option C with three significant figures to ensure that we have enough precision in our measurement.

Question 11

How many significant figures does the number 3 600 have?​

Accepted Answer

The number of significant figures in "3 600" cannot be determined without additional context or notation to indicate whether the zeros are significant or merely placeholders.

Question 12

A cereal box has the dimensions of 0.14 m × 0.22 m × 0.070 m.If there are 3.28 feet per meter,then what is the volume of the box in cubic feet?

Accepted Answer

The volume of the box in cubic meters is 0.14 m × 0.22 m × 0.070 m = 0.002156 cubic meters. To convert this to cubic feet, we multiply by (3.28 feet/meter)^3 = 27.648 feet^3/meter^3. Therefore, the volume of the box in cubic feet is 0.002156 cubic meters * 27.648 feet^3/meter^3 = 0.0596 cubic feet. This is closest to choice A, 7.6E-2 cubic feet.

Question 13

Multiplying a 2-significant-figure number by a 4-significant-figure number and then dividing the product by a seven-significant-figure number yields a number with how many significant figures?

Accepted Answer

When multiplying, the number of significant figures in the result is equal to the number of significant figures in the factor with the least number of significant figures. In this case, the 2-significant-figure number is the limiting factor. When dividing, the number of significant figures in the result is equal to the number of significant figures in the divisor. Therefore, the result will have 7 significant figures (the same as the divisor). However, since the product only has 2 significant figures, we must round the result to 2 significant figures, giving us a final answer with 2 significant figures.

Question 14

Volume can be measured in units of m³.Which of the following unit combinations also result in volume?

Accepted Answer

The answer of Volume can be measured in units of...

Question 15

The number 0.03 has how many significant figures?

Accepted Answer

The number 0.03 has two significant figures. The leading zeros are not counted as significant; only the '3' is significant, along with the zero that is between the decimal point and the '3'.

Question 16

The basic function of an automobile's carburetor is to atomize the gasoline and mix it with air to promote rapid combustion.Assume that 30.0 cm³ of gasoline is atomized into N spherical droplets.Each droplet has a radius of 1.0 × 10−⁵ m.Find the total surface area of these N spherical droplets.

Accepted Answer

The answer of The basic function of an automobile's carburetor...

Question 17

Modern electroplaters can cover a surface area of 75.0 m² with one troy ounce of gold (volume = 1.611 cm³).What is the thickness of the electroplated gold?

Accepted Answer

The correct answer is A because the thickness of the electroplated gold can be calculated using the formula: thickness = volume / (area * density). The density of gold is 19.32 g/cm^3. So, the thickness of the electroplated gold is: thickness = 1.611 cm^3 / (75.0 m^2 * 19.32 g/cm^3) = 2.15E-8 m.

Question 18

Assume when using a meter stick measuring can be done so that the last significant figure is in the tenth of a millimeter digit.If you are measuring an object with length between 6 and 7 cm,how many significant figures will result if you only use the part of the meter stick between the 1-cm and 9-cm positions?

Accepted Answer

Using the part of the meter stick between the 1-cm and 9-cm positions, the precision of the measurement is limited to the nearest millimeter, which is equivalent to one significant figure. Therefore, the length between 6 and 7 cm would have three significant figures.

Question 19

On planet Z,the standard unit of length is the foose.Ann the Astronaut is 5.2 feet tall on Earth.She lands on planet Z and is measured to be 88 foosi tall.Her partner Rachael is 92 foosi tall.How tall is Rachael on Earth?​

Accepted Answer

We can set up a proportion to relate the height of Ann and Rachael on Earth to their heights on planet Z.
5.2 ft / x = 88 foosi / 92 foosi
Cross-multiplying, we get:
88 * x = 5.2 * 92
Simplifying:
x = (5.2 * 92) / 88
x = 5.4 ft
Therefore, Rachael is 5.4 feet tall on Earth.

Question 20

Which one of the choices below represents the preferred practice regarding significant figures when adding the following: 15.9 + 14 + 77.68 + 6.898?

Accepted Answer

When adding numbers, the result should be rounded to the least number of decimal places in any of the numbers being added. Here, the number 14 has no decimal places, so the sum should be rounded to the nearest whole number, which is 114.

Quiz 1: Units, Trigonometry, and Vectors

Suppose an equation relating position,x,to time,t,is given by x = bt³ + ct⁴,where b and c are constants.The dimensions of b and c are respectively:

Which one of the choices below represents the preferred practice regarding significant figures when multiplying the following: 15.0 × 5.6 × 2.33?

When SI units are plugged into an equation,it is found that the units balance.Which of the following can we expect to be true for this equation?

A rectangular-shaped patio has a base length equal to (24.5 ± 0.2) m and a height equal to (9.3 ± 0.1) m.What is the area of the patio,including its uncertainty?

Calculate (0.83 + 0.049) (4.4 × 10³) ,keeping only significant figures.

A cement truck can pour 160 cubic yards of cement per hour.Express this in ft³/min.

The length and width of a standard sheet of paper is measured,and then the area is found by calculation to be 91.50 in.².The number of significant figures in the width measurement must be at least

How many significant figures does the number 3 600 have?

A cereal box has the dimensions of 0.14 m × 0.22 m × 0.070 m.If there are 3.28 feet per meter,then what is the volume of the box in cubic feet?

Multiplying a 2-significant-figure number by a 4-significant-figure number and then dividing the product by a seven-significant-figure number yields a number with how many significant figures?

Volume can be measured in units of m³.Which of the following unit combinations also result in volume?

The number 0.03 has how many significant figures?

Modern electroplaters can cover a surface area of 75.0 m² with one troy ounce of gold (volume = 1.611 cm³) .What is the thickness of the electroplated gold?

On planet Z,the standard unit of length is the foose.Ann the Astronaut is 5.2 feet tall on Earth.She lands on planet Z and is measured to be 88 foosi tall.Her partner Rachael is 92 foosi tall.How tall is Rachael on Earth?

Which one of the choices below represents the preferred practice regarding significant figures when adding the following: 15.9 + 14 + 77.68 + 6.898?

Quiz 1: Units, Trigonometry, and Vectors

Suppose an equation relating position,x,to time,t,is given by x = bt3 + ct4,where b and c are constants.The dimensions of b and c are respectively:

Which one of the choices below represents the preferred practice regarding significant figures when multiplying the following: 15.0 × 5.6 × 2.33?

When SI units are plugged into an equation,it is found that the units balance.Which of the following can we expect to be true for this equation?

​A rectangular-shaped patio has a base length equal to (24.5 ± 0.2) m and a height equal to (9.3 ± 0.1) m.What is the area of the patio,including its uncertainty?

Calculate (0.83 + 0.049) (4.4 × 103) ,keeping only significant figures.

A cement truck can pour 160 cubic yards of cement per hour.Express this in ft3/min.

The length and width of a standard sheet of paper is measured,and then the area is found by calculation to be 91.50 in.2.The number of significant figures in the width measurement must be at least

How many significant figures does the number 3 600 have?​

A cereal box has the dimensions of 0.14 m × 0.22 m × 0.070 m.If there are 3.28 feet per meter,then what is the volume of the box in cubic feet?

Multiplying a 2-significant-figure number by a 4-significant-figure number and then dividing the product by a seven-significant-figure number yields a number with how many significant figures?

Volume can be measured in units of m3.Which of the following unit combinations also result in volume?

The number 0.03 has how many significant figures?

Modern electroplaters can cover a surface area of 75.0 m2 with one troy ounce of gold (volume = 1.611 cm3) .What is the thickness of the electroplated gold?

On planet Z,the standard unit of length is the foose.Ann the Astronaut is 5.2 feet tall on Earth.She lands on planet Z and is measured to be 88 foosi tall.Her partner Rachael is 92 foosi tall.How tall is Rachael on Earth?​

Which one of the choices below represents the preferred practice regarding significant figures when adding the following: 15.9 + 14 + 77.68 + 6.898?

Suppose an equation relating position,x,to time,t,is given by x = bt³ + ct⁴,where b and c are constants.The dimensions of b and c are respectively:

A rectangular-shaped patio has a base length equal to (24.5 ± 0.2) m and a height equal to (9.3 ± 0.1) m.What is the area of the patio,including its uncertainty?

Calculate (0.83 + 0.049) (4.4 × 10³) ,keeping only significant figures.

A cement truck can pour 160 cubic yards of cement per hour.Express this in ft³/min.

The length and width of a standard sheet of paper is measured,and then the area is found by calculation to be 91.50 in.².The number of significant figures in the width measurement must be at least

How many significant figures does the number 3 600 have?

Volume can be measured in units of m³.Which of the following unit combinations also result in volume?

Modern electroplaters can cover a surface area of 75.0 m² with one troy ounce of gold (volume = 1.611 cm³) .What is the thickness of the electroplated gold?

On planet Z,the standard unit of length is the foose.Ann the Astronaut is 5.2 feet tall on Earth.She lands on planet Z and is measured to be 88 foosi tall.Her partner Rachael is 92 foosi tall.How tall is Rachael on Earth?