Question

Which numbers are rational? Check the three that apply.(3 points)
Responses

π
pi

70−−√
square root of 70

32−−√
square root of 32

1217
12 over 17

4.52525252...

Answer 1

A rational number is any number that can be expressed as a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \).

Let's analyze each option:

1. **π (pi)**: This number is an irrational number because it cannot be expressed as a fraction of two integers.

2. **\( \sqrt{70} \)**: This is also an irrational number because 70 is not a perfect square, meaning it cannot be expressed as a fraction of two integers.

3. **\( \sqrt{32} \)**: This can be simplified to \( \sqrt{16 \times 2} = 4\sqrt{2} \). Since \( \sqrt{2} \) is irrational, \( \sqrt{32} \) is also irrational.

4. **\( \frac{1217}{1} \)**: This can be written as a fraction of two integers (1217 and 1), making it a rational number.

5. **4.52525252...**: This is a repeating decimal, which can also be expressed as a fraction, thus it is a rational number.

Based on the analysis, the numbers that are rational are:

- \( \frac{1217}{1} \) (or 1217)
- 4.52525252...

So the three rational numbers are:

- \( \frac{1217}{1} \)
- 4.52525252...
And additionally, it could also include **0** or **1**, if they were part of the choices.

However, from the list provided, only **1217** and **4.52525252...** can be checked off as rational.