Is 6.8 a rational number?

Aug 11, 2016

Yes, $6.8$ is indeed a rational number.

Explanation:

By definition, a rational number is a number that can be expressed by the ratio $\frac{a}{b}$, where $a$ and $b$ are integers and $b$ doesn't equal $0$.

$6.8 = \frac{68}{10}$ and both 68 and 10 are integers.

In addition, $6.8$ is a rational number (part of many other numbers) that make up real numbers (others including terminating decimals, repeating decimals, integers, and counting numbers, which are all rational numbers).

Some examples include:

Counting Numbers: $\text{ } 0 , 1 , 2 , 3 , 4 , \ldots$

Integers: $\text{ } \ldots - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , \ldots .$

Rational Numbers: $\text{ } \frac{7}{9} , 8.47 , - \frac{5}{8} , 0.3 \ldots$

In conclusion, a number that doesn't meet these criteria would be otherwise considered an irrational number (a number that cannot be expressed in the form $\frac{a}{b}$ e.g. $1.341823 \ldots$, $\pi$, $\sqrt{2}$, etc.).

Irrational numbers are infinite, non-recurring decimals.