It may seem confusing at first to look for rational numbers between two identical numbers, such as 1 and 1. However, we can still find rational numbers that fit the criteria if we understand the concept of rational numbers.
A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In this case, we want to find numbers that can be represented between 1 and 1.
Some examples of rational numbers that can exist between 1 and 1 (essentially, we need to think of numbers that are very close to 1) are:
- 1.1
- 1.01
- 1.001
- 1.0001
- 1.00001
Each of these numbers is a rational number because they can be expressed as fractions. For instance, 1.1 can be represented as 11/10, 1.01 as 101/100, and so forth. While technically, there aren’t five rational numbers strictly between 1 and 1 as they are equal, we can still consider numbers that are infinitesimally close to 1.