HSPT Math : How to multiply and divide decimals

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #1 : How To Multiply And Divide Decimals

What is 48,570 in scientific notation?

Possible Answers:

\dpi{100} 4.857\times 10^{-4}

\dpi{100} 4.857\times 10^{4}

\dpi{100} 48.57\times 10^{4}

\dpi{100} 4.857\times 10^{2}

Correct answer:

\dpi{100} 4.857\times 10^{4}

Explanation:

Convert to scientific notation by creating a number that is greater than or equal to 1 AND less than 10 AND includes the same digits as the original number.  Remove all zeros before the first natural number and after the last natural number.

So, we have 48,570.

Now we move the decimal to create our number between 1 and 10.

4.8570

We have one zero after the last natural number, which is 7.  Remove that.

4.857

Now we must multiply that number by 10 to a certain power.  We choose our power by how many places the decimal must move to get our original number.  In this case, the decimal would have to move 4 places to the right.

4.857

48.57

485.7

4857.

48,570.

So our final answer is \dpi{100} 4.857\times 10^{4}

Example Question #2 : How To Multiply And Divide Decimals

Gradechart

If Exam 1 is worth 25% of the total grade, Exam 2 is worth 25% and Exam 3 is worth 50%, what is Dave’s final grade?

Possible Answers:

85.75

79

83.5

84

82

Correct answer:

84

Explanation:

Final Grade = Exam1 * 0.25 + Exam 2 * 0.25 + Exam3 * 0.50 =

96*0.25 + 70*0.25 + 85*0.5 =

24 + 17.5 + 42.5 = 84

Example Question #3 : How To Multiply And Divide Decimals

Kevin is looking at the blueprint of the house he is building. The scale is 1 inch = 5 feet. On paper, the master bedroom is 2.5 inches by 3 inches. What is the actual size of the bedroom?

Possible Answers:

20 ft x 30 ft

15 ft x 25 ft

7.5 ft x 9 ft

12.5 ft x 15 ft

10 ft x 10 ft

Correct answer:

12.5 ft x 15 ft

Explanation:

The given dimensions must be multiplied by 5, so 2.5 inches becomes 12.5 feet, and 3 inches becomes 15 feet.

Example Question #4 : How To Multiply And Divide Decimals

A car has gas mileage of 46 miles per gallon. Assume that gas costs $3.90 per gallon. What would be the total cost of gas if the car traveled 1,150 miles?

Possible Answers:

$179.40

$115.60

$97.50

$100.00

$125.70

Correct answer:

$97.50

Explanation:

First find out how many gallons of gas the car consumed while traveling 1150 miles. This can be found out like so:

1150 miles x gallons/46 miles = 25 gallons

Multiplying 25 by $3.90 yields $97.50.

Example Question #2 : How To Multiply And Divide Decimals

If , approximately how many inches are in one meter?

Possible Answers:

Correct answer:

Explanation:

and

Using the factor-label method we get the following equation.

We treat the units as if they are numbers, and can cancel the units from the fractions.

Example Question #3 : How To Multiply And Divide Decimals

You bought a dozen eggs marked at  and received  change from . What is the percent of sales tax?  

Possible Answers:

Correct answer:

Explanation:

Set the equation up as 

 

Solve for , which equals  

or

Therefore the percent sales tax is: 

Example Question #4 : How To Multiply And Divide Decimals

Multiply: 

Possible Answers:

Correct answer:

Explanation:

To multiply, there is no need to solve for a least common denominator.  Simply multiply the numerator with the numerator and the denominators together.

Example Question #5 : How To Multiply And Divide Decimals

Multiply:  

Possible Answers:

Correct answer:

Explanation:

Multiply the terms as is, ignoring the decimal.

Since there is one decimal from the original problem, the decimal place is one unit from the right.  Therefore, the final answer must have a decimal one unit to from the right.

The answer is .

Example Question #1 : How To Multiply And Divide Decimals

Menu 1

Above is the menu at the concession stand at a school carnival. 

David wants to buy some chicken strips for himself and his companions. He wants six strips, his brother Mickey wants five strips, his girlfriend Vickie wants three, and Mickey's girlfriend Jenny wants five. Since the concession stand only sells the strips in orders of four, he has decided to just purchase as many orders as it takes to feed the entire group. How much will he spend on enough orders of strips to satisfy the group?

(No tax is charged, since this is a school event)

Possible Answers:

Correct answer:

Explanation:

The group wants a total of  strips; since 

,

Dave will need to purchase five orders of strips (he cannot purchase a partial order). This will cost him

.

Example Question #2 : How To Multiply And Divide Decimals

An aircraft's cruising speed is  miles per hour. How far will it travel in hours?

Possible Answers:

 miles

 miles

 miles

 miles

Correct answer:

 miles

Explanation:

The formula to calculate distance is  where  represents rate of speed and  represents time.

In this problem,  mph., and   hours. 

Convert the  to an improper fraction:

 

To solve, multiply.

 miles.

At its cruising speed of  mph, the aircraft will travel  miles in   hours.

 

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