Recurring Decimals - (F.3)

There is no way to determine in general.

A rational number would result in either a fixed or recurring decimal.

There are infinite number of choices in the denominators.

2014-09-05 21:25:10 補充：
Nonetheless, for some common cases, you can have a note:

For example, 142857 refers to the recurring part with denominator as a multiple of 7.

2014-09-10 20:06:58 補充：
There is no way to determine in general.

A rational number would result in either a fixed or recurring decimal.

There are infinite number of choices in the denominators.

For example, as your case, there is one digit in the recurring decimal 0.3333333333 which is 1/3.

However, for 0.22222222222, there is also one digit here, but it is 2/9.

Of course for 1/3 you can view it as 3/9 and claim that every recurring decimal form by dividing by 9 would result in one-digit recurring.

However, for a more general situation, like you ask for 2-digit recurring, there are many different patterns of recurring with 2 digits, in general there should be no way to give a rule.

Still, this is a nice question to ask, thanks for your input.


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