## Making the Number System Easy to Grasp! | Branded Voices | Advertise – nativenewsonline.net

The Class 9 Maths Number System MCQs will help you understand the topic well, face the exam confidently, and score the best marks.

What is a number system? A number system is defined as representing numbers consistently using digits or symbols. There are different types of numbers, such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Let us see what each type of number is with some examples.

Natural numbers:  Natural numbers are numbers starting from 1 and ending to infinity. These are positive integer numbers. It includes all whole numbers except 0. These numbers are denoted by the letter N.

Example: 1,2,3,4,5…..

Whole numbers:  Whole numbers are natural numbers, including 0, so they are numbers starting from 0 and ending at infinity. They are all positive numbers. These numbers are denoted by the letter W.

Example: 0,1,2,3,4,5…..

Integers:  Integers are a set of negative numbers, positive numbers including 0. These numbers do not include decimal or fractional numbers. The letter Z denotes these numbers.

Example: 3, 0, -74, etc.

Rational numbers: Any number written in the form of x/y and y≠0 is known as a rational number. The letter Q denotes the rational numbers.

Example: 1/4, 6/8, ⅔, etc.,

There are infinite rational numbers in between any two given rational numbers. To understand this concept, let us see an example.

Example: Find five rational numbers between 2 and 3

We know to find a rational number between x and y, we add x and y and divide it by 2, i.e. x+y/2 so, x+y/2 is the number between x and y

The numbers are 5/2, 4/2, 7/4, 5/4, 1/2.

By looking at this, we realise there are infinite rational numbers between any two given rational numbers.

Irrational numbers: Any number that cannot be represented as a ratio is an irrational number.

Example: √3, √5, etc.

Real numbers: Real numbers consist of those numbers which are rational such as positive integers, negative integers, fractions, and irrational numbers. The letter R denotes these numbers.

Example: 3, 0, 1.8, 6/4, etc.

### Terminating and recurring (non-terminating) decimal numbers

Terminating decimal numbers: Terminating decimal numbers are, as the name says is a decimal number that has an end. If the decimal expression of a fraction x/y ends, then it is known as terminating decimal numbers. These numbers end after a specific number of digits after the decimal point. For example: ⅛ = 0.125, 0.35, 12.64

Recurring decimal numbers or repeating decimal numbers: Decimal numbers in which a number or a set of numbers repeat periodically after the decimal point.

Example: 46.374374374…. , 0.6666….

### Properties of rational numbers:

1. Rational numbers are represented either as a terminating decimal or a non-terminating decimal.
2. All terminating decimal Example: √5are rational numbers.
3. All non-terminating decimal expressions are rational numbers.

### Properties of irrational numbers:

1. The non-terminating decimal numbers are irrational.
2. If x is a positive number, which is not a perfect square, then √x (square root of x ) is an irrational number.</…….