Decimal Forms of Rational Numbers Here is the third step
Chapter 0, Problem P.1.76(choose chapter or problem)
Decimal Forms of Rational Numbers Here is the third step when we divide 1 by 17. (The first two steps are not shown, because the quotient is 0 in both cases.)
By convention we say that 1 is the first remainder in the long division process, 10 is the second, and 15 is the third remainder.
(a) Continue this long division process until a remainder is repeated, and complete the following table:
(b) Explain why the digits that occur in the quotient between the pair of repeating remainders determine the infinitely repeating portion of the decimal representation. In this case
\(\frac{1}{17}=0 . \overline{0588235294117647}\)
(c) Explain why this procedure will always determine the infinitely repeating portion of a rational number whose decimal representation does not terminate.
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