Thread: Repeating decimal

I have to give the sum of p+q where p/q is the reduced fraction represented by the repeating decimal
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1.36

Not sure where to go for this one.

Originally Posted by amanda1

I have to give the sum of p+q where p/q is the reduced fraction represented by the repeating decimal
__
1.36

Not sure where to go for this one.

Let x = 0.36363636363636....

Let's multiply x by 100:
100x = 36.3636363636363636....

Now let's subtract x from this:
100x - x = 36.3636363636363636... - 0.36363636363636... = 36

99x = 36

x = 36/99 = 4/11

So 1.363636363636... = 1 + 4/11 = 15/11

Thus p = 15 and q = 11.

Thus p + q = 26.

Note: Since 15/11 = 30/22, p + q could also be 52. Your answer is not unique.

-Dan

Hello, Amanda!

A slightly different approach . . .

Find the sum p+q where p/q is the reduced fraction
represented by the repeating decimal 1.363636...

Let N = 1.363636...

Multiply by 100: .100N .= .136.363636...
. . . Subtract N: . . . N .= . . .1.363636...

And we have: . . . 99N .= .135

Therefore: .N .= .135/99 .= .15/11 . . . and .p + q .= .26