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

Related problems in "Number Theory"

The problem asks to find the greatest common factor (G.C.F.) of the numbers 30, 45, and 60, given th...

Greatest Common FactorGCDPrime FactorizationInteger Properties
2025/5/26

The problem asks us to find which of the given numbers (11,116, 16,462, 21,240, 28,814) is divisible...

Divisibility RulesInteger PropertiesDivisibility by 2Divisibility by 3Divisibility by 6
2025/5/26

We are given that $x$, $y$, and $z$ are natural numbers such that $1 < x < y < z$, and we need to fi...

Diophantine EquationsInequalitiesInteger Solutions
2025/5/25

The problem asks us to find all triples of natural numbers $(x, y, z)$ such that $1 < x < y < z$ and...

Diophantine EquationsInequalitiesNumber Theory
2025/5/25

We are given that $x, y, z$ are natural numbers such that $1 < x < y < z$ and $(1 + \frac{1}{x})(1 +...

Diophantine EquationsInequalitiesInteger SolutionsNumber Theory
2025/5/25

We are given the HCF (highest common factor) and LCM (least common multiple) of two numbers, and one...

HCFLCMNumber Properties
2025/5/20

The problem consists of filling in the blanks in sentences related to number theory.

Number PropertiesEven NumbersOdd NumbersInteger Properties
2025/5/18

We are asked to find $\varphi(n)$ for $n \le 310$ and we are given $n = 4$. It is presumed we have t...

Euler's Totient FunctionNumber TheoryPrime Factorization
2025/5/7

The problem asks us to list the factors of the number 30. A factor of a number is an integer that di...

FactorsDivisibilityInteger Properties
2025/5/7

The problem asks to find the factors of 30.

FactorsDivisibilityInteger Properties
2025/5/7