Question

What type of number will result from 3.4059...−85
?(1 point)
Responses

Irrational, because both numbers are irrational.
Irrational, because both numbers are irrational.

Rational, because both numbers are rational.
Rational, because both numbers are rational.

Irrational, because one number is irrational.
Irrational, because one number is irrational.

Rational, because one number is rational.
Rational, because one number is rational.

Answer 1

To determine the type of number resulting from the operation \( 3.4059... - 85 \), we need to analyze the numbers involved.

- \( 3.4059... \) is a decimal that appears to be a repeating (or non-terminating) decimal, which suggests it may be an irrational number. However, we need to clarify: if it continues forever without repeating, then it would indeed be an irrational number. But if it is a rational number (which usually has repeating decimals), we could treat it as rational.
- \( 85 \) is a whole number, which is clearly a rational number.

Now, let's examine the operation:
- If \( 3.4059... \) is rational, then subtracting 85 (another rational number) from it will yield another rational number.
- If \( 3.4059... \) is irrational, subtracting 85 (rational) from it will result in an irrational number.

Given that repeating decimals are usually rational (like \( \frac{34}{10} \) as an example), it is more reasonable to classify \( 3.4059... \) as rational in this context, making the operation:
\[ \text{Rational number} - \text{Rational number} = \text{Rational number} \]

Hence, the correct response is:

**Rational, because both numbers are rational.**