Repeated and Nonrepeated Decimals

[mathdad]

My question concerns repeated and nonrepeated decimals. Are both rational numbers? Can you give an example for each?

 

[MarkFL]

My question concerns repeated and nonrepeated decimals. Are both rational numbers? Can you give an example for each?

A repeating decimal number is rational because you can always express such a number as the string of repeating digits over an equal number of 9's (one of the tricks my father taught me as a child). For example, we may write:

$$0.\overline{154}=\frac{154}{999}$$

A non-repeating decimal is irrational since it cannot be expressed as the ratio of one integer to another. $\sqrt{2}$ is an example of a non-repeating decimal.

 

[HallsofIvy]

You realize, I hope, that all decimals are either "repeating" or "non-repeating". So if it were true that "all repeated and non-repeated decimals are rational numbers" then there would be no irrational numbers!

 

[mathdad]

A repeating decimal number is rational because you can always express such a number as the string of repeating digits over an equal number of 9's (one of the tricks my father taught me as a child). For example, we may write:

$$0.\overline{154}=\frac{154}{999}$$

A non-repeating decimal is irrational since it cannot be expressed as the ratio of one integer to another. $\sqrt{2}$ is an example of a non-repeating decimal.

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