CONVERTING REPEATING DECIMALS TO FRACTIONS Take out a calculator!

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CONVERTING REPEATING DECIMALS TO FRACTIONS

Take out a calculator!


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)

116)

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

.7Rolling Pattern

13

23

9

Pattern11 Pattern

Write each as a decimal


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


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!


1399

0.13

2499

0.24

3699

0.36

13100

0.13

24100

0.24

Terminating

Terminating

36100

0.36 Terminating


Repeating

Repeating

Repeating


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!


THE END!Take out your

study guide


#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


12143413

=

=

=

=

50%

25%

75%

33.3%

=

=

=

=

66.6%

20%

40%

60%

23152535

#6


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.


CONVERTING REPEATING DECIMALS TO FRACTIONS

andMEMORIZING

DECIMAL EQUIVALENTS

Take out a calculator!


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)

116)

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

.7Rolling Pattern

13

23

9

Pattern11 Pattern

Write each as a decimal


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


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!


1399

0.13

2499

0.24

3699

0.36

13100

0.13

24100

0.24

Terminating

Terminating

36100

0.36 Terminating


Repeating

Repeating

Repeating


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!


2 = 50%1


4 = 25%1


4 = 75%3


3 =1 33.3%


3 =2 66.6%


5 =1 20%


5 =2 40%


5 =3 60%


5 =4 80%


THE END!Take out your

study guide

CONVERTING REPEATING DECIMALS TO FRACTIONS Take out a calculator!

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