Pre Algebra

1
Pre - Algebra Bench Mark 7 Know Rational Numbers
Are Either Terminating Or Repeating DecimalsWarm
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
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
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,
It is much less evident that repeating decimals
are also rational numbers.
For example,
So we can see that repeating decimals are also
rational numbers.
4
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 0.606060.
We will name our number a 0.606060
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 .606060
and multiply it by a power of 10,
10a 6.06060
The decimals do not line up so try multiplying by
100.
100a 60.6060
The decimals line up and the repeating parts will
cancel.
100a 60.606060
a 0.606060
-
20 33
99a 60
Solve for a and reduce.
5
Pre - Algebra Bench Mark 7 Know Rational Numbers
Are Either Terminating Or Repeating
DecimalsExample
1 11
Find the period of the repeating part of .
.
0
9
0
0
9
9
Divide.
0
0
0
0
0
- 99
1
0
0
- 99
0
1
0
- 99
1
We can see that 2 digits (0 and 9) are repeating
so the period is 2.
6
Pre - Algebra Bench Mark 7 Know Rational Numbers
Are Either Terminating Or Repeating
DecimalsPractice
4 9
a. Convert 0.4444 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 1.1818 repeating)
Classify the decimal as repeating or terminating.
19 18
d. Convert 1.0555 to a fraction in simplest
form.
(answer )
7
Pre - Algebra Bench Mark 7 Know Rational Numbers
Are Either Terminating Or Repeating DecimalsQuiz
7 8
1. Write as a decimal.
(answer 0.875 terminating)
Classify the decimal as repeating or terminating.
14 9
2. Convert 1.5555 to a fraction in simplest
form.
(answer )
3. Find the period of the repeating part of
.
(answer 1)
2 3
99 101
4. Convert 0.98019801 to a fraction in
simplest form.
(answer )
5. Find the period of the repeating part of
.
(answer 4)
85 101