Question

What type of number will result from 3.4059... - 8/5 Irrational, because one number is irrational. Rational, because one number is rational. Irrational, because both numbers are irrational. Rational, because both numbers are rational.

Answer 1

To determine whether the result of the expression \(3.4059... - \frac{8}{5}\) is rational or irrational, we first analyze the two numbers involved:

1. **\(3.4059...\)**: This is a decimal that appears to be a non-repeating decimal, which suggests it is an irrational number. However, it looks like it might also be a truncated or rounded representation of a rational number if it were to be more precisely defined with digits that repeat. As it is presented, we will treat \(3.4059...\) as a rational number since it can be represented as a decimal expansion of a rational number with a repeating nature.

2. **\(\frac{8}{5}\)**: This is a fraction, which is a rational number.

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

\[
\text{Rational} - \text{Rational} = \text{Rational}
\]

Thus, in this case:

- Since \(3.4059...\) can be interpreted as a rational number, and \(\frac{8}{5}\) is also rational, the result of \(3.4059... - \frac{8}{5}\) will also be a rational number.

The correct conclusion is:

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