1. Write as a decimal. 1 2 1. (answer: 0.5) 7 5 2. (answer: 1.4) 9 4 3.
Pre - Algebra
Bench Mark 7
Know Rational Numbers Are Either Terminating Or Repeating Decimals Warm Up
Write as a decimal. 1 2 1.
(answer: 0.5) 7 5 2.
(answer: 1.4) 9 4 3.
(answer: 2.25) 3 8 4.
(answer: 0.375)

2. Know Rational Numbers Are Either Terminating Or Repeating Decimals
Pre - Algebra
Bench Mark 7
Know Rational Numbers Are Either Terminating Or Repeating Decimals
Vocabulary:
rational number
number that can be expressed as a ratio of two integers
terminating decimal
number when expressed as a decimal has a
finite decimal expansion; also called a
regular number
repeating decimal
number when expressed as a decimal has
a ‘final’ set of digits which repeat an infinite
number of times; also called a recurring decimal
period
the number of recurring digits in a repeating
decimal; also called the repetend
vinculum
a horizontal line placed over the recurring digits in
a repeating decimal

3. Know Rational Numbers Are Either Terminating Or Repeating Decimals
Pre - Algebra
Bench Mark 7
Know Rational Numbers Are Either Terminating Or Repeating Decimals
It is obvious that terminating decimals are rational numbers.
For example,
0.75 = = 75
100 3 4
0.625 = =
625
1000 5 8
and 0.6 = = 6 10 3 5
It is much less evident that repeating decimals are also rational numbers.
For example, 1 9
= , 1 6 =
and = 4 11
So we can see that repeating decimals are also rational numbers.

4. Know Rational Numbers Are Either Terminating Or Repeating Decimals
Pre - Algebra
Bench Mark 7
Know Rational Numbers Are Either Terminating Or Repeating Decimals
The real challenge will be to write a fraction in simplest form given a repeating decimal.
To illustrate, lets make up a repeating decimal such as
We will name our number a =
and multiply it by a power of 10,
then subtract the original a and the new number
so that the repeating decimal parts
cancel each other in the subtraction.
a =
and multiply it by a power of 10,
10a =
The decimals do not line up so try multiplying by 100.
100a =
The decimals line up and the repeating parts will cancel.
100a =
a = 60 99 20 33 = -
a = 20 33
So, =
99a = 60
Solve for a and reduce.

5. Find the period of the repeating part of . . 9 9 9 Divide. 11 1.0 - 99
Pre - Algebra
Bench Mark 7
Know Rational Numbers Are Either Terminating Or Repeating Decimals Example 1 11
Find the period of the repeating part of . 9 9 9
Divide.
- 99 1
- 99 1
- 99 1
We can see that 2 digits (0 and 9) are repeating so the period is 2.

6. Classify the decimal as repeating or terminating.
Pre - Algebra
Bench Mark 7
Know Rational Numbers Are Either Terminating Or Repeating Decimals Practice 4 9
a. Convert to a fraction
in simplest form.
(answer: )
b. Find the period of
the repeating part of
(answer: 2 ) 32 33 13 11
c. Write as a decimal.
(answer: ; repeating)
Classify the decimal as repeating or terminating. 19 18
d. Convert to a fraction
in simplest form.
(answer: )

7. (answer: 0.875; terminating)
Pre - Algebra
Bench Mark 7
Know Rational Numbers Are Either Terminating Or Repeating Decimals Quiz 7 8
1. Write as a decimal.
(answer: 0.875; terminating)
Classify the decimal as repeating or terminating. 14 9
2. Convert to a fraction
in simplest form.
(answer: )
3. Find the period of
the repeating part of .
(answer: 1) 2 3 99
101
4. Convert to a
fraction in simplest form.
(answer: )
5. Find the period of
the repeating part of
(answer: 4) 85
101