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Problem 1

# Classify the number as to type. (For example, $$\frac{1}{2}$$ is rational and real, whereas $$\sqrt{5}$$ is irrational and real.) $$-3$$

Expert verified
The given number -3 is classified as rational and real.
See the step by step solution

## Step 1: Determine if the number is rational or irrational.

A number is considered rational if it can be expressed as a fraction (a/b) where a and b are integers, and b is not equal to 0. Since -3 can be expressed as a fraction $$-3/1$$ where both numerator and denominator are integers, we can classify -3 as a rational number.

## Step 2: Determine if the number is real or complex.

Real numbers include both rational and irrational numbers. In contrast, a complex number includes a real part and an imaginary part (in the form of $$a + bi$$, where a and b are real numbers, and i is the imaginary unit which is the square root of -1). Since -3 does not have an imaginary part and is a rational number, it is a real number.

## Step 3: Final Classification:

The given number -3 is rational and real.

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