What type of number will result from 3.4059...−8/5

Question

?(1 point)
Responses

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

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

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

Irrational, because one number is irrational.

Answer 1

To determine the type of number that results from the operation \( 3.4059... - \frac{8}{5} \), let's analyze the numbers involved:

1. 3.4059...: This number is a decimal that goes on forever, which suggests it might be a repeating or non-repeating decimal. However, since it has a finite number of non-repeating digits (3.4059) before the decimal suggests that it is a rational number (it can be expressed as a fraction).

2. \(\frac{8}{5}\): This is a fraction, which is clearly a rational number since it can be expressed as a ratio of two integers.

Now, when you subtract one rational number from another rational number:

• The result of subtracting two rational numbers is always rational.

Thus, \( 3.4059... - \frac{8}{5} \) will also be a rational number.

The correct response is:

Rational, because both numbers are rational.