Question

change the following decimal number in p/q from. 5.125125125125.......​

Answer 1

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Answer:

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Here's Ur answer...

1. 0.555555...

Let x be = 0.555555... --------(1)

Multiplying both sides by 10 since 1 number is repeating.

10 × x = 10 × 0.555555...

10x = 5.555555... --------(2)

Subtract equation (1) from equation (2)

10x - x = 5.5555555... - 0.555555...

9x = 5

x = 5/9

p/q form of 0.555555... is 5/9

2. 0.3636363636...

Let x be = 0.36363636... --------(1)

Multiplying both sides by 100 since 2 numbers are repeating.

100 × x = 100 × 0.36363636...

100x = 36.36363636... --------(2)

Subtract equation (1) from equation (2)

100x - x = 36.36363636... - 0.36363636...

99x = 36

x = 36/99

x = 12/33

x = 4/11

p/q form of 0.36363636... is 4/11

3. 3.888888...

Let x be = 3.888888... --------(1)

Multiplying both sides by 10 since 1 number is repeating.

10 × x = 10 × 3.888888...

10x = 38.888888... --------(2)

Subract equation (1) from equation (2)

10x - x = 38.88888... - 3.88888...

9x = 35

x = 35/9

p/q form of 3.88888... is 35/9

Hope this helps..!!

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