 # Converting Rational Numbers to Decimals Using Long Division

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Videos, examples, lessons, and solutions to help Grade 7 students learn how to convert rational numbers to decimals using long division.

### New York State Common Core Math Grade 7, Module 2, Lesson 14

Lesson 14 Student Outcomes

• Students understand that every rational number can be converted to a decimal.

• Students represent fractions as decimal numbers that either terminate in zeros or repeat, and students represent repeating decimals using, a bar over the shortest sequence of repeating digits.

• Students interpret word problems and convert between fraction and decimal forms of rational numbers.

Lesson 14 Summary

The real world requires that we represent rational numbers in different ways depending on the context of a situation. All rational numbers can be represented as either terminating decimals or repeating decimals using the long division algorithm. We represent repeating decimals by placing a bar over the shortest sequence of repeating digits.

Example 1: Can All Rational Numbers Be Written as Decimals?

a. Using the division button on your calculator, explore various quotients of integers 1 through 11. Record your fraction representations and their corresponding decimal representations in the space below.

b. What two types of decimals do you see?

Example 2: Decimal Representations of Rational Numbers

In the chart below, organize the fractions and their corresponding decimal representation listed in Example 1 according to their type of decimal.

Example 3: Converting Rational Numbers to Decimals Using Long-Division

Use the long division algorithm to find the decimal value of - 3/4

Exercise 1

Convert each rational number to its decimal form using long division.

a. - 7/8
b. 3/16

Example 4: Converting Rational Numbers to Decimals Using Long-Division

Use long division to find the decimal representation of 1/3.

Exercise 2

Calculate the decimal values of the fraction below using long division. Express your answers using bars over the shortest sequence of repeating digits.

a. - 4/9
b. - 1/11
c. 1/7
d. - 5/6

Example 5: Fractions Represent Terminating or Repeating Decimals

How do we determine whether the decimal representation of a quotient of two integers, with the divisor not equal to zero, will terminate or repeat?

Example 6: Using Rational Number Conversions in Problem Solving

a. Eric and four of his friends are taking a trip across the New York State Thruway. They decide to split the cost of tolls equally. If the total cost of tolls is \$8, how much will each person have to pay?

b. Just before leaving on the trip, two of Eric’s friends have a family emergency and cannot go. What is each person’s share of the \$8 tolls now?

Lesson 14 Problem Set

2. Chandler tells Aubrey that the decimal value of - 1/17 is not a repeating decimal. Should Aubrey believe him?
Explain.

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