Question
Explain why 1/3 is called a rational number. How do you know
Answers
GPT-4o mini
A rational number is defined as any number that can be expressed as the quotient or fraction \( \frac{a}{b} \) of two integers, where \( a \) is the numerator and \( b \) is the denominator, and \( b \) is not equal to zero.
The fraction \( \frac{1}{3} \) is called a rational number because:
1. It can be expressed as the quotient of two integers: Here, \( 1 \) (the numerator) and \( 3 \) (the denominator) are both integers.
2. The denominator is not zero: In this case, the denominator is \( 3 \), which is indeed not zero.
Since both conditions are satisfied, \( \frac{1}{3} \) qualifies as a rational number.
Additionally, rational numbers can be represented as terminating or repeating decimals. The decimal form of \( \frac{1}{3} \) is \( 0.333... \), which is a repeating decimal. This further confirms its classification as a rational number.
The fraction \( \frac{1}{3} \) is called a rational number because:
1. It can be expressed as the quotient of two integers: Here, \( 1 \) (the numerator) and \( 3 \) (the denominator) are both integers.
2. The denominator is not zero: In this case, the denominator is \( 3 \), which is indeed not zero.
Since both conditions are satisfied, \( \frac{1}{3} \) qualifies as a rational number.
Additionally, rational numbers can be represented as terminating or repeating decimals. The decimal form of \( \frac{1}{3} \) is \( 0.333... \), which is a repeating decimal. This further confirms its classification as a rational number.