Michelle needs to determine the rational numbers from the choices below. Which of the following numbers are rational?

Select THREE correct answers.
A.15−−√

B.83

C.65%

D.17−−√

E.788


To determine which numbers are rational, let's briefly review what makes a number rational. A rational number can be expressed as a fraction \(\frac{a}{b}\) where \(a\) and \(b\) are integers, and \(b \neq 0\). In other words, any number that can be written as a fraction is rational.

Let's analyze each option:

A. \(\sqrt{15}\)  
   - \(\sqrt{15}\) is not a perfect square, so it cannot be expressed as a simple fraction. It is an **irrational** number.

B. \(\frac{8}{3}\)  
   - \(\frac{8}{3}\) is already in the form of a fraction \(\frac{a}{b}\), where both \(a = 8\) and \(b = 3\) are integers. Thus, it is a **rational** number.

C. \(65\%\)  
   - \(65\%\) is equivalent to \(\frac{65}{100} = \frac{13}{20}\), which is a fraction with both numerator and denominator as integers. Thus, it is a **rational** number.

D. \(\sqrt{17}\)  
   - \(\sqrt{17}\) is not a perfect square, so it cannot be expressed as a simple fraction. It is an **irrational** number.

E. \(788\)  
   - \(788\) is an integer, and any integer can be expressed as a fraction with a denominator of 1 (i.e., \(\frac{788}{1}\)). Thus, it is a **rational** number.

**Correct answers:**
- **B.** \(\frac{8}{3}\)
- **C.** \(65\%\)
- **E.** \(788\)

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Identify if \(\sqrt{25}\) is a rational number.
2. Which of the following is a rational number: \(\pi\), \(\frac{1}{2}\), \(e\)?
3. Convert 0.75 to a fraction and determine if it's rational.
4. Is \(\frac{\sqrt{4}}{2}\) a rational number?
5. Determine if \(-5\) is a rational number.

**Tip:** Remember, a number is rational if it can be written as a fraction of two integers. This includes all integers and finite decimals!

Explore the concept of rational numbers and determine which numbers among choices A, B, C, D, and E are rational. This problem covers identifying rational numbers as fractions of integers and includes analysis of square roots and percentages.

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