Identifying Rational Numbers Between -1.36 and -1.35

Introduction

Identifying rational numbers between two intervals can be both fascinating and practical. This article explains how to find rational numbers between -1.36 and -1.35, and provides examples and methods to illustrate the process.

Understanding Intervals and Rational Numbers

The intervals -1.36 and -1.35 represent ranges of real numbers. Specifically, the interval -1.36 includes all real numbers from -1.36 to -1 inclusive, and the interval -1.35 includes all real numbers from -1.35 to -1 inclusive. The rational numbers that exist between these two intervals are all the rational numbers within the range -1 to -1.35 inclusive.

Examples of Rational Numbers in the Interval

Some examples of rational numbers in this range include:

-1 -0.99 -0.5 0 0.5 1 1.5 2... 34.5 -1.35

So, any rational number between -1 and -1.35 would fit between the given intervals.

Creating More Specific Rational Numbers

For a more specific set of rational numbers, consider the following variations:

-1.351, -1.352, -1.353, -1.354, -1.355, -1.356, -1.357, -1.38, -1.359

Since these numbers differ by 0.001, you can also generate rational numbers by adding a positive rational number smaller than 0.001 to -1.35 and making it negative, such as:

-1.3500625 (which is -1.35 1/16000)

Using Fractions

If you prefer fractions, note that 1.35 27/20. Here are some fractions between -1.36 and -1.35:

{87}{64} {53}{39} {72}{53} {91}{67} {19}{14} {99}{73} {80}{59} {61}{45} {42}{31} {65}{48} {88}{65} {23}{17} {96}{71} {73}{54} {50}{37} {77}{57}

Using the Average of Two Integers

Another method is to calculate the average of two rational numbers. For example:

[frac{-1.36 - 1.35}{2} frac{-2.71}{2} -1.355]

General Approach

Any number you can write in ordinary decimal notation is rational. For example, 1.55 155/100. Although you can reduce the fraction, the core idea is that any rational number can be expressed as the ratio of two integers. Therefore, to find a rational number between -1.36 and -1.35, simply write down a number that satisfies the inequalities. For instance:

-1.351 is a perfectly valid answer.

Note that the notation of the decimal separator (point or comma) does not change the meaning of the number; both commas and points are commonly used internationally.