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## #1 2013-01-29 06:01:43

Reek
Member
Registered: 2010-12-22
Posts: 11

### Is a non-repeating and non-terminating decimal always an irrational?

We can build 1/33 like this, .030303..... (03 repeats). .030303.... tends to 1/33 .
So,I was wondering this: In the decimal representation, if we start writing the 10 numerals in such a way that the decimal portion never ends and never repeats; then am I getting closer and closer to some irrational number?

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## #2 2013-01-29 06:09:21

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,743

### Re: Is a non-repeating and non-terminating decimal always an irrational?

hi Reek

Yes.

Terminating decimals can be converted to fractions.

Recurring decimals can be converted to fractions.

All the rest are irrational.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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