Questions: Name the rational numbers from the list below. -5, 0, 59, 6.43, √15, √81, 6 1/2, -1/3, 1.3939939993…

Solution Steps

To identify rational numbers from the list, we need to determine which numbers can be expressed as a fraction of two integers. Rational numbers include integers, fractions, and terminating or repeating decimals. We will check each number in the list to see if it fits these criteria.

We are given the following list of numbers: \[ -5, 0, 59, 6.43, \sqrt{15}, \sqrt{81}, 6 \frac{1}{2}, -\frac{1}{3}, 1.3939939993 \]

A rational number can be expressed as \( \frac{p}{q} \) where \( p \) and \( q \) are integers and \( q \neq 0 \). We will analyze each number in the list:

• \( -5 \) is an integer, hence rational.
• \( 0 \) is an integer, hence rational.
• \( 59 \) is an integer, hence rational.
• \( 6.43 \) is a terminating decimal, hence rational.
• \( \sqrt{15} \) is an irrational number.
• \( \sqrt{81} = 9 \) is an integer, hence rational.
• \( 6 \frac{1}{2} = 6.5 \) is a terminating decimal, hence rational.
• \( -\frac{1}{3} \) is a fraction, hence rational.
• \( 1.3939939993 \) is a non-terminating decimal, hence irrational.

From the analysis, the rational numbers identified are: \[ -5, 0, 59, 6.43, 9, 6.5, -\frac{1}{3} \]

Final Answer