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copyright©amberpasillas2010
CONVERTING REPEATING DECIMALS TO FRACTIONS
Take out a calculator!
copyright©amberpasillas2010
1)
72
)7
a
b
3)
74
)75
)76
)77
)7
c
d
e
f
g
1)
92
)93
)94
)95
)96
)97
)9
a
b
c
d
e
f
g
1)
112
)113
)114
)115
)11
6)
117
)118
)11
a
b
c
d
e
f
g
h
1
.09
.18
.27
.36
.45
.54
.63
.72
.142857
.285714
.428571
.571428
.714285
.857142
.1111 = .1
.2222 = .2
.3333 = .3
.4444 = .4
.5555 = .5
.6666 = .6
.7
Rolling Pattern
1
3
2
3
9 Pattern11
Pattern
Write each as a decimal
copyright©amberpasillas2010
19
0.1
29
0.2
39
0.3
13
110
0.1
210
0.2
Terminating
Terminating
310
0.3 Terminating
What do you notice about the repeating decimals compared to the terminating decimals?
Repeating
Repeating
Repeating
copyright©amberpasillas2010
19
0.1
29
0.2
39
0.3
13
110
0.1
210
0.2
Terminating
Terminating
310
0.3 Terminating
Repeating
Repeating
Repeating
49 0.4
59 0.5
69
0.6 23
Writing Repeating Decimals as fractions can be a challenge. But following a pattern really helps!
copyright©amberpasillas2010
1399
0.13
2499
0.24
3699
0.36
13100
0.13
24100
0.24
Terminating
Terminating
36100
0.36 Terminating
What do you notice about the repeating decimals compared to the terminating decimals?
Repeating
Repeating
Repeating
copyright©amberpasillas2010
123999
0.123
21549999
0.2154
56
0.83
1231000
0.123
215410000
0.2154
Terminating
Terminating
83100
0.83 Terminating
Try these challenging ones!
Repeating
Repeating
RepeatingWhen one digit is terminating this can be a challenge!
copyright©amberpasillas2010
THE END!Take out your
study guide
copyright©amberpasillas2010
#5
one tenth0.1
19
0.1
110
one less than 10 repeating
22 hundredths0.22 22100
2299
0.22 one less than 100 repeating
three tenths0.3
39
0.3
310
one less than 10repeating
123 thousandths0.123 123
1000
123999
0.123 one less than 1000repeating3
3 13
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12143413
=
=
=
=
50%
25%
75%
33.3%
=
=
=
=
66.6%
20%
40%
60%
23152535
#6
copyright©amberpasillas2010
TEACHER NOTE: The following slides on memorize these
equivalents were used in Algebra Readiness but saved for later in Pre-Algebra for when you teach
Percents.
copyright©amberpasillas2010
CONVERTING REPEATING DECIMALS TO FRACTIONS
andMEMORIZING
DECIMAL EQUIVALENTS
Take out a calculator!
copyright©amberpasillas2010
1)
72
)7
a
b
3)
74
)75
)76
)77
)7
c
d
e
f
g
1)
92
)93
)94
)95
)96
)97
)9
a
b
c
d
e
f
g
1)
112
)113
)114
)115
)11
6)
117
)118
)11
a
b
c
d
e
f
g
h
1
.09
.18
.27
.36
.45
.54
.63
.72
.142857
.285714
.428571
.571428
.714285
.857142
.1111 = .1
.2222 = .2
.3333 = .3
.4444 = .4
.5555 = .5
.6666 = .6
.7
Rolling Pattern
1
3
2
3
9 Pattern11
Pattern
Write each as a decimal
copyright©amberpasillas2010
19
0.1
29
0.2
39
0.3
13
110
0.1
210
0.2
Terminating
Terminating
310
0.3 Terminating
What do you notice about the repeating decimals compared to the terminating decimals?
Repeating
Repeating
Repeating
copyright©amberpasillas2010
19
0.1
29
0.2
39
0.3
13
110
0.1
210
0.2
Terminating
Terminating
310
0.3 Terminating
Repeating
Repeating
Repeating
49 0.4
59 0.5
69
0.6 23
Writing Repeating Decimals as fractions can be a challenge. But following a pattern really helps!
copyright©amberpasillas2010
1399
0.13
2499
0.24
3699
0.36
13100
0.13
24100
0.24
Terminating
Terminating
36100
0.36 Terminating
What do you notice about the repeating decimals compared to the terminating decimals?
Repeating
Repeating
Repeating
copyright©amberpasillas2010
123999
0.123
21549999
0.2154
56
0.83
1231000
0.123
215410000
0.2154
Terminating
Terminating
83100
0.83 Terminating
Try these challenging ones!
Repeating
Repeating
RepeatingWhen one digit is terminating this can be a challenge!
copyright©amberpasillas2010
2 = 50%1
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4 = 25%1
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4 = 75%3
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3 =1 33.3%
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3 =2 66.6%
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5 =1 20%
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5 =2 40%
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5 =3 60%
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5 =4 80%
copyright©amberpasillas2010
THE END!Take out your
study guide
