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.
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