To determine whether the number 0.2 is a rational number, let's go through the steps to find out if it can be expressed as a fraction of two integers:
1. Understanding Rational Numbers: A rational number is any number that can be expressed as the quotient or fraction [tex]\(\frac{a}{b}\)[/tex] of two integers, where [tex]\(a\)[/tex] (the numerator) and [tex]\(b\)[/tex] (the denominator) are integers, and [tex]\(b \neq 0\)[/tex].
2. Expressing 0.2 as a Fraction:
- The decimal number 0.2 can be written as [tex]\(\frac{2}{10}\)[/tex].
- Both 2 and 10 are integers, and 10 is not zero.
3. Simplifying the Fraction:
- The fraction [tex]\(\frac{2}{10}\)[/tex] can be simplified by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 2.
- Simplifying, we get: [tex]\(\frac{2 \div 2}{10 \div 2} = \frac{1}{5}\)[/tex].
4. Conclusion: Since 0.2 can be written as the fraction [tex]\(\frac{1}{5}\)[/tex], where both 1 and 5 are integers and 5 is not zero, 0.2 is indeed a rational number.
Therefore, the correct answer to the question is:
A. True
