**Let’s first start with the definition of rational numbers. I know that definitions in Mathematics appear to be boring but remember, they are the foundations of mathematics. The strength of your foundation will decide the heights of your mathematical concepts.**

**So let’s start with the definition.**

**A number ‘r’ is called a rational number, if it can be written in **** form (p/q) where p and q are integers and q≠0**

**And there is one more interesting fact related to rational numbers. It is that non-terminating repeating decimal is a rational number. So obviously, every non-terminating repeating decimal expansion can be represented in **** form (p/q) where p and q are integers and q≠0**

**Let’s observe this with the help of an example**

**Let a non-terminating repeating decimal expansion be 0.635635……**

**Let x=0.635635……**

**Multiply both sides by 1000**

**1000x=635.635………**

**1000x=635+x where x=0.635635……**

**999x=635**

**x = **(635/999)

**Where p=635 and q=999**