Convert Between Fractions and Decimals

Decimals and Fractions

Learning Objectives

By the end of this section, you will be able to:

Convert fractions to decimals

Order decimals and fractions

Simplify expressions using the order of operations

Find the circumference and area of circles

Convert a Fraction to a Decimal

To convert a fraction to a decimal, divide the numerator of the fraction by the denominator of the fraction.

Convert Fractions to Decimals

Write the fraction 3/4 as a decimal.

Write the fraction as a decimal: 1/4

Write the fraction as a decimal: 3/8

.

Repeating Decimal

A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly.

Order Decimals and Fractions

In Decimals, we compared two decimals and determined which was larger. To compare a decimal to a fraction, we will first convert the fraction to a decimal and then compare the decimals.

Simplify Expressions Using the Order of Operations

Simplify the expressions:

ⓐ7(18.3−21.7)

ⓑ23(8.3−3.8)

Simplify:

ⓐ8(14.6−37.5)

ⓑ3/5(9.6−2.1).

Simplify:

ⓐ25(25.69−56.74)

ⓑ2/7(11.9−4.2).

Find the Circumference and Area of Circles

Determine Whether a Decimal is a Solution of an Equation

Solving equations with decimals is important in our everyday lives because money is usually written with decimals.

Solve Equations with Decimals

Multiple Choice

What is the radius of this circle?

• 18
• 36
• 9
• 8

Multiple Choice

What is the area of the yellow?

• 78.5 mi²
• 19.625 mi²
• 39.25 mi²
• 31.4 mi²

Multiple Choice

The homeowners association wants to enclose the playground in a fence. How much fencing will they need to purchase? Is this question finding the area or the circumference?

• area
• circumference
• neither

Multiple Choice

Randy’s circular garden has a radius of 1.5 feet. He wants to enclose the garden edging that costs $0.75 per foot. About how much will the edging cost? 

• $8.00
• $7.00
• $3.50
• $0.50

Multiple Choice

Daniel wants to buy cookies for her friend. The
radius of a cookie is 5 inches. What is the distance around the cookie?

• 10 in
• 2.5 in
• 15.7 in
• 31.4 in 

Multiple Choice

Find the area of the circle

• 43.96
• 153.86 
• 87.82
• 307.72

Multiple Select

Which fraction and decimal are equivalent? Choose all that apply.

• $$\frac{4}{10}$$ and 0.04

• $$\frac{6}{100}$$ and 0.60

• $$\frac{3}{10}$$ and 0.3

• $$\frac{9}{100}$$ and 0.09

Multiple Choice

Model A is shaded to represent a value that is less than 1 whole.
Choose Yes or No to indicate whether the value of the shaded part of Model A is equivalent to $$\frac{8}{10}$$  

• Yes

• No

Multiple Choice

Is the number sentence True or False?

0.3 = $$\frac{3}{100}$$  

• True

• False

Multiple Select

Which of the following names the same number as 0.62? Choose all that apply.

• sixty-two hundredths

• six tenths and 2 hundredths

• $$\frac{62}{10}$$

• $$\frac{62}{100}$$

Multiple Select

What is 0.5 written as a fraction? Choose all that apply.

• $$\frac{5}{100}$$

• $$\frac{5}{10}$$

• $$\frac{50}{100}$$

• $$\frac{50}{10}$$

Multiple Choice

Rylie correctly answered 9 questions out of 10 on a test. What fraction of the test questions did Rylie answer incorrectly?

• $$\frac{9}{10}$$

• $$\frac{9}{100}$$

• $$\frac{1}{10}$$

• $$\frac{1}{100}$$

Multiple Choice

Is the number below equivalent to $$\frac{15}{100}$$  ?


fifteen hundredths

• Yes

• No