Let's convert the decimal [tex]\(0.2\)[/tex] to a fraction and reduce it to its simplest form.
Step-by-Step Solution:
1. Express the Decimal as a Fraction:
The decimal [tex]\(0.2\)[/tex] can be written as a fraction with a denominator of 10. So, we start by expressing it as:
[tex]\[
0.2 = \frac{2}{10}
\][/tex]
2. Simplify the Fraction:
To simplify the fraction [tex]\(\frac{2}{10}\)[/tex], we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 2 and 10 is 2. We divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{2 \div 2}{10 \div 2} = \frac{1}{5}
\][/tex]
3. Result:
Thus, the fraction [tex]\(\frac{2}{10}\)[/tex] simplifies to [tex]\(\frac{1}{5}\)[/tex].
After converting the decimal [tex]\(0.2\)[/tex] to a fraction and simplifying it, we obtain the simplest form:
[tex]\[
0.2 = \frac{1}{5}
\][/tex]
Therefore, the correct answer is:
a. [tex]\(\frac{1}{5}\)[/tex]
