The Number System
Changing Repeating
Decimals to Fractions
Guided Notes
FIVE Practice Problems
8.NS.1
FREEBIE
This product includes a guided notes
page for students to glue in their
notebooks. The notes take students
through a series of steps to use in
order to change a repeating decimal
to a fraction.
Following the note page, students
will work on five problems. One
example is provided for the
assignment. A variety of repeating
decimals (one digit, two digits, etc.)
is given for students to complete.
Cut along the dotted line and glue these notes in your notebook.
Notes: Changing Repeating Decimals to Fractions
Change .𝟏 to a decimal.
Change .7𝟏𝟒 to a decimal.
Step 1: Let x = .11111
Step 1: Let x = .7141414
Step 2: Ask yourself how many
numbers repeat. Since one
number repeats, we will use 10x
for our second equation. Multiply
both sides of your first
equation(x and .11111) by 10. Your
new equation will be equal to
10x = 1.11111
Step 2: Ask yourself how many
numbers repeat. Since two
numbers repeat, we will use 100x
for our second equation. Multiply
both sides of your first
equation(x and .7141414) by 100.
Your new equation will be equal
to 100x = 71.41414
If two numbers repeated (.36),
we would use 100x = 36.3636 for
our second equation.
If three numbers repeated
(.123), we would use
1000x = 123.123123 for our
second equation.
Step 3: Subtract your original
equation from your new equation.
(Line up the decimals.)
10x = 1.11111
- x = .11111
9x =1
Step 3: Subtract your original
equation from your new equation.
(Line up the decimals.)
100x = 71.4141414
- x=
.7141414
99x = 70.7
Step 4: Solve for x.
Step 4: Solve for x.
9𝑥
1
99𝑥
9
99
9
=
=
70.7
99
Step 5: Check your solution.
Step 5: Check your solution.
1
70.7
9
= .1
99
=
707
990
= .714
© The Clever Clover, 2014
Changing Repeating
Name:
Decimals to Fractions Hour:
Directions: Change the following repeating decimals to
fractions. Reduce fractions to lowest terms.
Example) 0.7
Let x stand for 0.7 or 0.77777
Let 10x stand for 7. 7 or 7.77777
10x = 7.77777
- x = .77777
9x = 7
Answer:
9 9
0.36
𝟕
𝟗
Answer:
.16
.2
Answer:
Answer:
Bonus:
.5
.142857
Answer:
Answer:
© The Clever Clover, 2014
Changing Repeating
Name:
Decimals to Fractions Hour:
Directions: Change the following repeating decimals to
fractions. Reduce fractions to lowest terms.
Example) 0.7
Let x stand for 0.7 or 0.77777
Let 10x stand for 7. 7 or 7.77777
10x = 7.77777
- x = .77777
9x = 7
Answer:
9 9
𝟕
𝟗
0.36
100x = 36.3636
- x = .3636
99x = 36
99 99
Answer:
=
𝟏𝟓
𝟗𝟎
=
𝟒
𝟏𝟏
.16
.2
10x = 2.2222
- x = .2222
9x = 2
9 9
10x = 1.6666
- x = .1666
9x = 1.5 = 15
9
9
90
Answer:
Answer:
𝟐
𝟗
Bonus:
.5
9
142857
1,000,000x = 142857.142857
x=
.142857
999,999x = 142,857 = 1
999,999
999,999 7
10x = 5.5555
- x = .5555
9x = 5
9
𝟑𝟔
𝟗𝟗
Answer:
𝟓
𝟗
Answer:
© The Clever Clover, 2014
𝟏
𝟕
𝟏
𝟔
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