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

Guest Sep 15, 2017

#1**+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

#1**+1 **

Best Answer

\(\frac{3}{7}\) 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