To determine whether the number [tex]\(0.4\)[/tex] is a rational number, let's analyze the information provided.
1. Understanding the number [tex]\(0.4\)[/tex]:
- The decimal number [tex]\(0.4\)[/tex] can indeed be represented as the fraction [tex]\(\frac{4}{10}\)[/tex].
2. Simplifying the fraction:
- We can simplify the fraction [tex]\(\frac{4}{10}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
- [tex]\(\frac{4 \div 2}{10 \div 2} = \frac{2}{5}\)[/tex].
3. Definition of a rational number:
- 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].
4. Checking the result:
- The fraction [tex]\(\frac{2}{5}\)[/tex] fits the definition of a rational number because:
- It is expressed as a quotient of two integers: [tex]\(2\)[/tex] (numerator) and [tex]\(5\)[/tex] (denominator).
- The denominator [tex]\(5\)[/tex] is not zero.
Therefore, since [tex]\(0.4\)[/tex] can be expressed as the fraction [tex]\(\frac{2}{5}\)[/tex], which is a ratio of two integers, it is indeed a rational number.
Hence, the statement "The number 0.4 can be written as [tex]\(\frac{4}{10}\)[/tex], so it is a rational number." is
True.
Answer: A. True.
