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.

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

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

Rational, because both numbers are rational.

Answer 1

To determine the type of number that results from the operation \( 3.4059... - 85 \), we first need to classify the numbers involved in the operation:

1. **Rational Numbers**: A number is rational if it can be expressed as a fraction of two integers (i.e., \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \)).

2. **Irrational Numbers**: A number is irrational if it cannot be expressed as a fraction of two integers.

The number \( 3.4059... \) is a decimal that terminates and has a repeating pattern, which indicates it can be expressed as a fraction. Therefore, \( 3.4059... \) is a rational number.

The number \( 85 \) is also a rational number, as it can be expressed as \( \frac{85}{1} \).

Now, when we subtract one rational number from another (in this case, \( 3.4059... \) from \( 85 \)), the result is also a rational number.

Thus, the correct response is:

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