Question

Choose which group of sets the following number belongs to. Be sure to account for ALL sets.
five eighths
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Part 1
A.
real​ numbers, rational numbers
B.
real​ numbers, irrational numbers
C.
real​ numbers, rational​ numbers, natural numbers
D.
rational​ numbers, natural​ numbers, integers
E.
irrational​ numbers, natural numbers

Answer 1

The number "five eighths" can be represented as the fraction \( \frac{5}{8} \).

Let's analyze what groups it belongs to:

1. **Real Numbers**: All rational and irrational numbers belong to the real numbers. Since \( \frac{5}{8} \) is a rational number, it is also a real number.

2. **Rational Numbers**: A rational number is defined as any number that can be expressed as a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \). Since \( \frac{5}{8} \) fits this definition, it is a rational number.

3. **Irrational Numbers**: These are numbers that cannot be expressed as a fraction of two integers. Since \( \frac{5}{8} \) can be expressed as a fraction, it is not an irrational number.

4. **Natural Numbers**: These are positive integers (1, 2, 3, ...). Since \( \frac{5}{8} \) is a fraction and not a whole number, it is not a natural number.

5. **Integers**: These are whole numbers including positive numbers, negative numbers, and zero. Again, since \( \frac{5}{8} \) is a fraction, it is not an integer.

Now, let's review the options:

A. real numbers, rational numbers - **This is true.**
B. real numbers, irrational numbers - **This is false.**
C. real numbers, rational numbers, natural numbers - **This is false (not a natural number).**
D. rational numbers, natural numbers, integers - **This is false (not a natural number or an integer).**
E. irrational numbers, natural numbers - **This is false.**

The correct answer is: **A. real​ numbers, rational numbers.**