# Converting Between Fractions and Decimals Using Equivalent Fractions

Examples, videos, and solutions to help Grade 7 students learn how to convert between fractions and decimals using equivalent fractions.

### New York State Common Core Math Module 2, Grade 7, Lesson 13

Lesson 13 Student Outcomes

Students understand that the context of a real-life situation often determines whether a rational number should be represented as a fraction or decimal.

Students understand that decimals specify points on the number line by repeatedly subdividing intervals into tenths (deci- means one-tenth).

Students convert positive decimals to fractions and fractions to decimals when the denominator is a product of only factors of 2 and/or 5.

Lesson 13 Summary

Any terminating decimal can be converted to a fraction using place value (e.g.,0.35 is thirty-five hundredths or 35/100). A fraction whose denominator includes only factors of and can be converted to a decimal by writing the denominator as a power of ten.

Example 1: Representations of Rational Numbers in the Real World

Following the opening activity and class discussion, describe why we need to know how to represent rational numbers in different ways.

Example 2: Using Place Values to Write (Terminating) Decimals as Equivalent Fractions

a. What is the value of the number 2.25? How can this number be written as a fraction or mixed number?
b. Rewrite the fraction in its simplest form showing all steps that you use.
c. What is the value of the number 2.025? How can this number be written as a mixed number?
d. Rewrite the fraction in its simplest form showing all steps that you use.

Exercise 1

Use place value to convert each terminating decimal to a fraction. Then rewrite each fraction in its simplest form.

a. 0.218
b. 0.16
c. 2.72
d. 0.0005

Example 3: Converting Fractions to Decimals—Fractions with Denominators Having Factors of only 2 and/or 5.

a. What are “decimals”?
b. Use the meaning of decimal to relate decimal place values.
c. Write the number 3/100 as a decimal. Describe your process.
d. Write the number 3/20 as a decimal. Describe your process.
e. Write the number 10/25 as a decimal. Describe your process.
f. Write the number 8/40 as a decimal. Describe your process.

Exercise 2

Convert each fraction to a decimal using an equivalent fraction.

a. 3/16
b. 7/5
c. 11/32
d. 35/50

Lesson 13 Problem Set

1. Convert each terminating decimal to a fraction in its simplest form.
a. 0.4
b. 0.16
c. 0.625
d. 0.08
e. 0.012

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 