# Is .6 a rational number?

Sep 13, 2016

A rational number is a number, which can be described as a ratio of two integers. As it is a ratio of integers, it can be positive as well as negative.

Further, any decimal fraction, which limits itself beyond the decimal point (such as $5.7$ which does not go beyond tenth place) or has continuously repeats numbers (till infinity) beyond a certain place of decimal (such as $4.33333 \ldots .$ or $0.232142857142857142857 \ldots .$) can be easily written as ratio of integers, however large and hence are rational.

Now as $0.6 = \frac{6}{10}$, is a ratio of two integers, it is a rational number.

Sep 18, 2016

$0.6 \text{ is a rational number}$

#### Explanation:

The basic rule: does it satisfy one of 2 conditions.

$\textcolor{b l u e}{\text{Condition 1}}$ Is it a terminating decimal?

Example: 0.125 This stops after the 5 so it terminates

$\textcolor{w h i t e}{.}$

$\textcolor{b l u e}{\text{Condition 2}}$ Is it a repeating decimal

Example: 0.356356356356....

written as $0.356 \overline{356}$
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$\textcolor{o l i v e}{\text{If the decimal satisfies either of these 2 conditions then, yes.}}$
$\textcolor{o l i v e}{\text{A rational number is a number that can be written in the form of a fraction}}$

$\textcolor{m a \ge n t a}{\text{By the way the counting numbers are rational}}$

$\textcolor{m a \ge n t a}{\frac{1}{1} \text{; "2/1"; "3/1"; "4/1...."& so on}}$
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$\textcolor{red}{\text{Answering your question}}$

$0.6 = \frac{6}{10}$ as this can be written as a fraction it is a rational number.