Question 1

If a circle has a radius of 1.109 m,what is its area expressed to the correct number of significant figures?

Accepted Answer

The area of a circle is calculated using the formula $A = \pi r^2$, where $r$ is the radius. Substituting the given radius, $1.109$ m, we get $A = \pi (1.109)^2$. Calculating this gives an area of approximately $3.86379$ m^2. However, since the radius is given to four significant figures, the area should also be reported to four significant figures, making the correct answer $3.864$ m^2.

Question 2

Which of the following numbers is the smallest?

Accepted Answer

The answer of Which of the following numbers is the...

Question 3

What is the sum of 2.67 + 1.976 + 2.1 expressed to the correct number of significant figures?

Accepted Answer

The sum of 2.67 + 1.976 + 2.1 is 6.746, but it should be expressed with the least number of decimal places of the numbers added, which is 1 decimal place, making the correct answer 6.7.

Question 4

The length and width of a rectangle are 1.125 m and 0.606 m,respectively.Multiplying,your calculator gives the product as 0.68175.Rounding properly to the correct number of significant figures,the area of the rectangle should be written as

Accepted Answer

The correct rounding based on the significant figures of the given measurements (1.125 and 0.606, both with 4 significant figures) results in the product being reported with 4 significant figures as well, which is 0.682.

Question 5

What is 0.205^2/3,to the correct number of significant figures?

Accepted Answer

The answer of What is 0.205^2/3,to the correct number of...

Question 6

What is the sum of 1.53 + 2.786 + 3.3 expressed to the correct number of significant figures?

Accepted Answer

The sum of 1.53 + 2.786 + 3.3 is 7.616. However, the correct number of significant figures is determined by the least precise measurement, which in this case is 3.3 (having only one decimal place). Therefore, the sum should be expressed as 7.6 to match this precision.

Question 7

Using a digital balance the mass of a certain piece of wood is read as 12.946 g.Thinking in terms of accuracy and significant figures,what value would you record on your data sheet if the balance is accurate to one-tenth of a gram?

Accepted Answer

The balance is accurate to one-tenth of a gram, so the mass should be recorded with one decimal place, which is 12.9 g.

Question 8

Which one of the following numbers is equivalent to the number 0.0001776?

Accepted Answer

To convert 0.0001776 to scientific notation, you move the decimal point 4 places to the right, making it 1.776. This is multiplied by 10 raised to the power of -4 to account for the decimal shift, resulting in 1.776 × 10^-4.

Question 9

What is the difference between 103.5 and 102.24 expressed to the correct number of significant figures?

Accepted Answer

The difference between 103.5 and 102.24 is 1.26, but since the least number of decimal places in the given numbers is 1 (103.5), the difference should also be expressed to 1 decimal place, making it 1.3.

Question 10

Write out the number 8.42 × 10^-5 in full with a decimal point and correct number of zeros.

Accepted Answer

To convert scientific notation to standard notation, move the decimal point to the left for negative powers of 10 and to the right for positive powers of 10. In this case, the power of 10 is negative, so we move the decimal 5 places to the left, resulting in 0.0000842.

Question 11

A dog has three puppies.Spot weighs 12 ounces.Rascal weighs 9.5 ounces.Socks weighs 10.2 ounces.What is the total weight of the litter expressed to the correct number of significant figures?

Accepted Answer

The total weight of the puppies is 12 + 9.5 + 10.2 = 31.7 ounces. However, since the weights of the puppies are given with at most two significant figures (9.5 and 10.2), the total should also be expressed with two significant figures, rounding 31.7 to 32 ounces.

Question 12

To get to her physics class,Alice walks 0.25 mi to the bus stop.She takes the bus 1.2 mi to the train station.She takes the train 13 mi and walks the remaining 0.17 mi to her class.How far is her commute expressed to the correct number of significant figures?

Accepted Answer

The distances given are to two significant figures, so the total distance should also be expressed to two significant figures. Adding the distances: 0.25 mi + 1.2 mi + 13 mi + 0.17 mi = 14.62 mi, which to two significant figures is 15 mi.

Question 13

Add 1,299g and 45.1kg, And express your answer in milligrams (mg)to the correct number of significant figures.

Accepted Answer

To add 1,299g and 45.1kg, first convert 45.1kg to grams: 45.1kg = 45,100g. Then add: 1,299g + 45,100g = 46,399g. Convert to milligrams: 46,399g = 46,399,000mg. Expressed in scientific notation with correct significant figures, it is 4.64 × 10^7 mg.

Question 14

A train travels at a constant speed of 60.4 mi/h for 101.5 min.What distance does the train cover expressed to the correct number of significant figures?

Accepted Answer

The answer of A train travels at a constant speed...

Question 15

What is the result,expressed to the proper number of significant figures,of adding 23.4 to 91.237 and then subtracting 23.4?

Accepted Answer

The answer of What is the result,expressed to the proper...

Question 16

The last page of a book is numbered 764.The book is 3.0 cm thick,not including its covers.What is the average thickness (in centimeters)of a page in the book,rounded to the proper number of significant figures?

Accepted Answer

To find the average thickness of a page, we need to divide the total thickness of the book (3.0 cm) by the total number of pages (764). 
Average thickness = 3.0 cm/ 764 pages = 0.00393 cm/page = 0.0079 cm (rounded to two significant figures). 
Therefore, the best choice is C.

Question 17

What is 56 + 
Written with the correct number of significant figures?

Accepted Answer

The answer of What is 56 + 
Written with the...

Question 18

A rectangular garden measures 15 m long and 13.70 m wide.What is the length of a diagonal from one corner of the garden to the other?

Accepted Answer

We can use the Pythagorean theorem to find the length of the diagonal. The diagonal will form the hypotenuse of a right triangle with the length and width of the garden forming the other two sides.

Using the Pythagorean theorem:

a^2 + b^2 = c^2

Where a and b are the length and width of the garden, and c is the length of the diagonal.

15^2 + 13.70^2 = c^2

225 + 187.69 = c^2

412.69 = c^2

c ≈ 20

Therefore, the length of the diagonal is approximately 20 meters.

The closest answer choice is C, which is 20 meters.

Question 19

A traveler has about $536 in his checking account,about $2107 in his savings account and exactly $7.62 in his wallet.To the greatest precision warranted,how much money does this shopper have?

Accepted Answer

The answer of A traveler has about $536 in his...

Question 20

The length and width of a rectangle are 1.125 m and 0.606 m,respectively.You calculate the rectangle's perimeter by adding these numbers and multiplying by two.Your calculator's display reads 3.462.To the correct number of significant figures,the perimeter should be written as

Accepted Answer

The answer of The length and width of a rectangle...

Quiz 1: Introduction to Physics

If a circle has a radius of 1.109 m,what is its area expressed to the correct number of significant figures?

Which of the following numbers is the smallest?

What is the sum of 2.67 + 1.976 + 2.1 expressed to the correct number of significant figures?

The length and width of a rectangle are 1.125 m and 0.606 m,respectively.Multiplying,your calculator gives the product as 0.68175.Rounding properly to the correct number of significant figures,the area of the rectangle should be written as

What is 0.205^2/3,to the correct number of significant figures?

What is the sum of 1.53 + 2.786 + 3.3 expressed to the correct number of significant figures?

Using a digital balance the mass of a certain piece of wood is read as 12.946 g.Thinking in terms of accuracy and significant figures,what value would you record on your data sheet if the balance is accurate to one-tenth of a gram?

Which one of the following numbers is equivalent to the number 0.0001776?

What is the difference between 103.5 and 102.24 expressed to the correct number of significant figures?

Write out the number 8.42 × 10^-5 in full with a decimal point and correct number of zeros.

A dog has three puppies.Spot weighs 12 ounces.Rascal weighs 9.5 ounces.Socks weighs 10.2 ounces.What is the total weight of the litter expressed to the correct number of significant figures?

To get to her physics class,Alice walks 0.25 mi to the bus stop.She takes the bus 1.2 mi to the train station.She takes the train 13 mi and walks the remaining 0.17 mi to her class.How far is her commute expressed to the correct number of significant figures?

Add 1,299g and 45.1kg, And express your answer in milligrams (mg) to the correct number of significant figures.

A train travels at a constant speed of 60.4 mi/h for 101.5 min.What distance does the train cover expressed to the correct number of significant figures?

What is the result,expressed to the proper number of significant figures,of adding 23.4 to 91.237 and then subtracting 23.4?

The last page of a book is numbered 764.The book is 3.0 cm thick,not including its covers.What is the average thickness (in centimeters) of a page in the book,rounded to the proper number of significant figures?

What is 56 + Written with the correct number of significant figures?

A rectangular garden measures 15 m long and 13.70 m wide.What is the length of a diagonal from one corner of the garden to the other?

A traveler has about $536 in his checking account,about $2107 in his savings account and exactly $7.62 in his wallet.To the greatest precision warranted,how much money does this shopper have?

The length and width of a rectangle are 1.125 m and 0.606 m,respectively.You calculate the rectangle's perimeter by adding these numbers and multiplying by two.Your calculator's display reads 3.462.To the correct number of significant figures,the perimeter should be written as

Quiz 1: Introduction to Physics

If a circle has a radius of 1.109 m,what is its area expressed to the correct number of significant figures?

Which of the following numbers is the smallest?

What is the sum of 2.67 + 1.976 + 2.1 expressed to the correct number of significant figures?

The length and width of a rectangle are 1.125 m and 0.606 m,respectively.Multiplying,your calculator gives the product as 0.68175.Rounding properly to the correct number of significant figures,the area of the rectangle should be written as

What is 0.2052/3,to the correct number of significant figures?

What is the sum of 1.53 + 2.786 + 3.3 expressed to the correct number of significant figures?

Using a digital balance the mass of a certain piece of wood is read as 12.946 g.Thinking in terms of accuracy and significant figures,what value would you record on your data sheet if the balance is accurate to one-tenth of a gram?

Which one of the following numbers is equivalent to the number 0.0001776?

What is the difference between 103.5 and 102.24 expressed to the correct number of significant figures?

Write out the number 8.42 × 10-5 in full with a decimal point and correct number of zeros.

A dog has three puppies.Spot weighs 12 ounces.Rascal weighs 9.5 ounces.Socks weighs 10.2 ounces.What is the total weight of the litter expressed to the correct number of significant figures?

To get to her physics class,Alice walks 0.25 mi to the bus stop.She takes the bus 1.2 mi to the train station.She takes the train 13 mi and walks the remaining 0.17 mi to her class.How far is her commute expressed to the correct number of significant figures?

Add 1,299g and 45.1kg, And express your answer in milligrams (mg) to the correct number of significant figures.

A train travels at a constant speed of 60.4 mi/h for 101.5 min.What distance does the train cover expressed to the correct number of significant figures?

What is the result,expressed to the proper number of significant figures,of adding 23.4 to 91.237 and then subtracting 23.4?

The last page of a book is numbered 764.The book is 3.0 cm thick,not including its covers.What is the average thickness (in centimeters) of a page in the book,rounded to the proper number of significant figures?

What is 56 + Written with the correct number of significant figures?

A rectangular garden measures 15 m long and 13.70 m wide.What is the length of a diagonal from one corner of the garden to the other?

A traveler has about $536 in his checking account,about $2107 in his savings account and exactly $7.62 in his wallet.To the greatest precision warranted,how much money does this shopper have?

The length and width of a rectangle are 1.125 m and 0.606 m,respectively.You calculate the rectangle's perimeter by adding these numbers and multiplying by two.Your calculator's display reads 3.462.To the correct number of significant figures,the perimeter should be written as

What is 0.205^2/3,to the correct number of significant figures?

Write out the number 8.42 × 10^-5 in full with a decimal point and correct number of zeros.