Question

Which product is rational? (1 point)
10•8
8• square root 25
12• pi
12•5.3420941

Answer 1

Choose the number that fits into all the following number sets: natural number, whole number, integer. (1 point)
8
Pi
-3/5
5.3

Answer 2

A rational product is one that can be expressed as a fraction of two integers.

Let's analyze the options:

1. **10 • 8** = 80 (rational)
2. **8 • square root 25** = 8 • 5 = 40 (rational)
3. **12 • pi** (approximately 37.699) (irrational, since π is irrational)
4. **12 • 5.3420941** (approximately 64.10513) (rational, as it is a product of integers and a rational number)

From these analyses, the rational products are:

- 10 • 8
- 8 • square root 25
- 12 • 5.3420941

The only irrational product is **12 • pi**.

Thus, the products that are rational are **10 • 8**, **8 • square root 25**, and **12 • 5.3420941**.

Answer 3

To determine which number fits into all the specified number sets (natural numbers, whole numbers, and integers), let's analyze each option:

1. **8**:
- Natural Number: Yes (natural numbers are positive integers: 1, 2, 3, ...)
- Whole Number: Yes (whole numbers include 0 and all natural numbers)
- Integer: Yes (integers include all whole numbers and their negatives)

2. **Pi (π)**:
- Natural Number: No (π is not an integer)
- Whole Number: No (π is not an integer)
- Integer: No (π is not an integer)

3. **-3/5**:
- Natural Number: No (negative numbers are not natural numbers)
- Whole Number: No (whole numbers are non-negative)
- Integer: No (it’s a fraction, not an integer)

4. **5.3**:
- Natural Number: No (not an integer)
- Whole Number: No (not an integer)
- Integer: No (not an integer)

Given this analysis, the only number that fits into all three sets (natural numbers, whole numbers, and integers) is **8**.