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# Is 3/7 a rational number?

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I tried it online but everyone says it is rational when it keeps repeating itself. Please help me out.

Sep 15, 2017

#1
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$$\frac{3}{7}$$ is a rational number.

In order to be classified as a rational number, a number must meet the following condition:

A number is rational if and only if you can represent that number with $$\frac{a}{b}$$ where $$a,b\in\mathbb{Z}$$. 3/7 meets this rule; a=3 and b=7.

Another way to think about it is the following:

A number is rational if and only if its decimal expansion either terminates OR repeats indefinitely. $$\frac{3}{7}=0.\overline{428571}$$, which repeats indefinitely. This is a rational number.

Sep 15, 2017

#1
+2337
+1

$$\frac{3}{7}$$ is a rational number.

In order to be classified as a rational number, a number must meet the following condition:

A number is rational if and only if you can represent that number with $$\frac{a}{b}$$ where $$a,b\in\mathbb{Z}$$. 3/7 meets this rule; a=3 and b=7.

Another way to think about it is the following:

A number is rational if and only if its decimal expansion either terminates OR repeats indefinitely. $$\frac{3}{7}=0.\overline{428571}$$, which repeats indefinitely. This is a rational number.

TheXSquaredFactor Sep 15, 2017