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(a)

1. Let x = the repeating decimal. (a) x = 0.151 515 151 5…

2. Multiply

x by the power of 10 that

contains the same number of zeros as

there are digits in the repeating pattern.

The pattern contains 2 digits so

multiply by 100.

100

x = 15.151 515 15…

3. Subtract

x from the new value. 100x - x = 15.151 515 15 - 0.151 515 15

99

x = 15

4. Solve the linear equation found, putting

your answer in simplest (improper if

necessary) fraction form.

x

=

=

5. Check your answer by doing the division

on your calculator.

5

÷ 33 = 0.15151515…

(b)

1. Let x = the repeating decimal. (b) x = 1.244 444 44…

2. Multiply

x by the power of 10 that

contains the same number of zeros as

there are digits in the repeating pattern.

The pattern contains 1 digit so

multiply by 10.

10

x = 12.444 444…

3. Subtract

x from the new value. 10x - x = 12.444 444 - 1.244 444

9

x = 11.2

4. Solve the linear equation found, putting

your answer in simplest (improper if

necessary) fraction form.

x

= = =

5. Check your answer on your calculator. 56

÷ 45 = 1.244 44…

(c)

1. Let x = the repeating decimal. (c) x = 0.114 211 421 142…

2. Multiply

x by the power of 10 that

contains the same number of zeros as

there are digits in the repeating pattern.

The pattern contains 4 digits so

multiply by 10 000.

10 000

x = 1142.114 211 421 142…

3. Subtract

x from the new value. 10 000x - x = 1142.114 211 421 142

- 0.114 211 421 142

9999

x = 1142

4. Solve the linear equation found, putting

your answer in simplest (improper if

necessary) fraction form.

x

=

5. Check your answer on your calculator. 1142

÷ 9999 = 0.114 211 421 142…

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