class IX Number System

5. This is the process of converting an *irrational number* into a *rational number*.
8. numbers* This collection includes all *natural numbers* and *zero, and is denoted by the symbol **W*.
9. line* This is a visual representation of *numbers* extending infinitely in both positive and negative directions.
10. recurring* This type of *decimal expansion* continues indefinitely with a *repeating block of digits*, such as 1/3 which equals 0.333... or 1/7 which equals 0.142857....
11. numbers* These are the *counting numbers* starting from 1, and their collection is denoted by the symbol *N*.
12. This set consists of all *whole numbers* and their *negative counterparts,along with the number zero and it is denoted by the symbol **Z*,

1. This type of *decimal expansion* ends after a *finite number of digits*, as seen with the rational number 7/8 which equals 0.875.
2. expansion* This is the representation of a number using a base-ten system, which for rational numbers is either *terminating* or *non-terminating recurring*.
3. numbers* This collection encompasses all *rational* and *irrational numbers, and is denoted by **R*. Every real number is represented by a unique point on the number line.
4. non-recurring* This type of *decimal expansion* continues indefinitely *without any repeating block of digits, and is characteristic of **irrational numbers* like 0.10110111011110....
6. numbers* A number ‘s’ is called *irrational* if it *cannot be written in the form p/q, where p and q are integers and q ≠ 0. Examples include *√2** and *π*.
7. root* For a positive real number a, *√a = b means b² = a* and b > 0. For example, if a is 4, then b is 2 because 2² equals 4.
8. numbers* A number ‘r’ is called a *rational number* if it can be written in the form *p/q, where p and q are integers and q ≠ 0. This collection includes natural numbers, whole numbers, and integers, and the symbol **Q* is used to denote them.