Rational Numbers and
Decimal Expansions
Presented by Mr. Laws
8th Math
JCMS

8.NS.1“ Know that numbers that are not
rational are called irrational. Understand
informally that every number has a
decimal expansion; for rational numbers
show that decimal expansion repeats
eventually, and convert a decimal
expansion which repeats eventually into a
rational number.”
Goal/ Objective

Using math principles, explain how I
determine if fractions have terminating or
repeating decimals; and how do I convert
them into a decimal expansion that
repeats.
Essential Question

Rational numbers can be expressed as a
fraction, where the numerator and
denominator are integers but the
denominator can’t equal to zero.
𝑎
where b ≠ 0
𝑏
Rational Numbers as Fractions
Rational numbers as fractions can be
either terminating decimals or
repeating decimals, which can be found
by dividing the numerator by the
denominator.
For example:

5
10
1
3
= 0.5 = 5 ÷ 10 (terminating decimal)
= 0.3333… = 1÷ 3 (repeating decimal)
Rational Numbers as Fractions

To change a decimal to a fraction, you
write the number over the place value for
example: .355
. 3
5
10ths 100rds
5
1000ths
=
355
1000
=
71
200
Note: Remember reduce all fractions to its lowest term!
Changing Decimals to Fractions

To change a fraction to decimal, just
divide numerator by the denominator:
4
7
0.5714285
= 7 4.0000000
In order to solve, you must keep adding zeros
until it begins to repeat or stops.
How do I convert fractions to
decimals.

To convert repeating decimals into fractions, use the
following rule:
◦ Single digit repeating decimals in the tenth
place will always go over a denominator of 9.
◦ Example:
4
.4 
9
.3 
3 1

9 3
11
2
 1  1.2
9
9
◦ Double digit repeating decimals in the 100th place will
always go over a denominator of 99.
◦ Example:
27 3
.27 

99 11
54 6
.54 

99 11
100
1
 1  1.1
99
9
Converting Repeating Decimals
Another way to convert repeating decimals to fractions is to
use the algebraic method.
Example
1. Convert .45 into a fraction.

Let n = .45 Since there is 2 digits multiply the equation by
100 on both sides.
100n  45.45
n
.45
________________
99n 45 5


99 99 11
Using Algebra to Convert
Repeating Decimals
What are some important concepts to
remember about the lesson?
 Are you able to answer the essential
question?
 Is there anything else you would like to
learn about converting decimals to
fractions or fractions to decimals?

Ouestions /Summary