Rational Numbers: Fractions, Decimals, and Percents Worksheet

Question 1

Convert 3/5 to a decimal and a percent.

Accepted Answer

The fraction 3/5 is equal to 0.6 because 3 divided by 5 is 0.6. It is equal to 60% because 0.6 times 100 is 60.

Question 2

Convert 0.375 to a fraction in simplest form and to a percent.

Accepted Answer

The decimal 0.375 is equal to 375/1000, which simplifies to 3/8. It is equal to 37.5% because 0.375 times 100 is 37.5.

Question 3

Convert 72% to a decimal and a fraction in simplest form.

Accepted Answer

The percent 72% is equal to 0.72 as a decimal. It is equal to 72/100, which simplifies to 18/25.

Question 4

Order these rational numbers from least to greatest: 0.45, 2/5, 48%, 0.5.

Accepted Answer

The numbers from least to greatest are 2/5, 0.45, 48%, and 0.5. This is because 2/5 equals 0.4, 48% equals 0.48, and 0.5 is already in decimal form.

Question 5

Which is greater, 7/8 or 85%? Explain how you know.

Accepted Answer

The fraction 7/8 is greater than 85%. Since 7 divided by 8 is 0.875, it is equal to 87.5%, which is greater than 85%.

Question 6

A class has 30 students. If 40% of the students ride the bus, how many students ride the bus?

Accepted Answer

There are 12 students who ride the bus. This is because 40% of 30 is 0.40 times 30, which equals 12.

Question 7

A store is selling a backpack for $48. It is discounted by 25%. What is the sale price?

Accepted Answer

The sale price is $36. The discount is 25% of $48, which is $12, so $48 minus $12 equals $36.

Question 8

A recipe uses 3/4 cup of sugar. You want to make half the recipe. How much sugar should you use?

Accepted Answer

You should use 3/8 cup of sugar. Half of 3/4 is found by multiplying 3/4 by 1/2, which equals 3/8.

Question 9

Convert 1/6 to a decimal. State whether the decimal terminates or repeats.

Accepted Answer

The fraction 1/6 is equal to 0.1666... . The decimal repeats because the digit 6 continues without ending.

Question 10

A student scored 18 out of 24 points on a quiz. Write the score as a fraction in simplest form, a decimal, and a percent.

Accepted Answer

The score as a fraction is 18/24, which simplifies to 3/4. As a decimal, it is 0.75, and as a percent, it is 75%.

Question 11

Use the table to answer the question: A survey shows that 12 students chose soccer, 8 chose basketball, and 5 chose tennis as their favorite sport. What percent of the students chose basketball?

Accepted Answer

32% of the students chose basketball. There are 25 students total, and 8/25 equals 0.32, which is 32%.

Question 12

Place 5/8, 0.7, and 60% on a number line from 0 to 1. Then list them from least to greatest.

Accepted Answer

The numbers from least to greatest are 60%, 5/8, and 0.7. This is because 60% equals 0.60, 5/8 equals 0.625, and 0.7 equals 0.70.

Question 13

A $60 video game has a sales tax of 7.5%. What is the total cost after tax?

Accepted Answer

The total cost is $64.50. The tax is 7.5% of $60, which is 0.075 times 60, or $4.50, so the total is $60 plus $4.50.

Question 14

A bottle is 2/3 full. After some water is poured in, it is 90% full. By what fraction of the bottle did the amount of water increase?

Accepted Answer

The amount of water increased by 7/30 of the bottle. Since 90% equals 9/10, the increase is 9/10 minus 2/3, which equals 27/30 minus 20/30, or 7/30.

Question 15

Explain why 0.2, 1/5, and 20% all represent the same rational number.

Accepted Answer

They all represent the same rational number because 1 divided by 5 equals 0.2, and 0.2 as a percent is 20%. Each form names the same amount, which is one fifth of a whole.

Rational Numbers: Fractions, Decimals, and Percents

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