The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 2.5: Expressing Rational Numbers

as Decimals

A common error students make when writing rational numbers as decimals is failing to realize

whether a decimal repeats or, if they do realize it repeats, not identifying the correct sequence of

repeating digits. Negative numbers can add to the confusion.

1. Explain that all rational numbers can be represented as a terminating decimal or a repeating
   decimal. Note that a terminating decimal has no remainder and that a repeating decimal
   will always have a remainder. A repeating decimal will also always have a number or group
   of numbers that repeat. (You might want to mention that, although they are not rational
   numbers, there are decimals that are nonterminating and nonrepeating. These are called
   irrational numbers. The numberπis an example.)


2. Review the steps for expressing rational numbers as decimals and the examples on the work-
   sheet with your students. Depending on their abilities, you may find it necessary to show the
   steps for long division. Remind your students that they must place a bar over the repetend,
   which is the number or numbers that repeat.


3. Emphasize that for negative fractions students must use the fraction’s absolute value when
   dividing the numerator by the denominator. They must then remember to place the negative
   sign in their answer. Depending on the abilities of your students, you may find it helpful to
   review absolute value. See 1.14: ‘‘Finding Absolute Values and Opposites.’’

EXTRA HELP:

Calculators may express fractions as decimals incorrectly. Some calculators either round the

decimal to a given place or omit digits after a certain place.

ANSWER KEY:

(1)0.16 (2)− 0. 6 (3)− 0. 16 (4)− 0. 4 (5)0.45 (6)0.1875 (7)− 0. 416 (8) 0. 428571

(9) 0. 90 (10)− 0. 1 (11) 0. 714285 (12)−0.25

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(Challenge) 0 .3 is greater than 0.3. Explanations may vary. A possible explanation is that 0.3

is equal to

3

10

, and that 0.3isequalto

3

10

+

3

100

+

3

1000

....

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56 THE ALGEBRA TEACHER’S GUIDE