Question 660283
Suppose you have 1/9 which is
0.1111111111 . . . to infinity
If you are just given this repeating decimal, how
do you convert it back to 1/9?
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First, say
x = .1111111 . . .
and
10x = 1.11111 . . .
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Now do this subtraction:
10x = 1.11111 . . .
    -x = .1111111 . . .
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9x = 1
x = 1/9
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Suppose you had 7/11 = .636363636 . . .
x = .6363636 . . .
100x = 63.636363 . . .
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Do the subtraction:
100x = 63.636363 . . .
        -x = .6363636 . . .
99x = 63
x = 63/99
x  = (7/11)x(9/9)
x = 7/11
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hope this helps