The problem asks whether the number $7.11$ is rational or irrational.

Number TheoryRational NumbersIrrational NumbersNumber Representation
2025/3/21

1. Problem Description

The problem asks whether the number 7.117.11 is rational or irrational.

2. Solution Steps

A rational number is a number that can be expressed as a fraction pq\frac{p}{q}, where pp and qq are integers and q0q \neq 0. An irrational number cannot be expressed in this form.
The given number is 7.117.11.
We can write 7.117.11 as a fraction by multiplying and dividing by 100:
7.11=7.11×100100=7111007.11 = \frac{7.11 \times 100}{100} = \frac{711}{100}
Since 711711 and 100100 are both integers, 7.117.11 can be written as a fraction of two integers. Therefore, 7.117.11 is a rational number.

3. Final Answer

Rational

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