Question

Explain :-

Rational numbers – definition, number system, rational numbers on number line, types with examples.​

Answer 1

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Rational numbers: A rational number is that number which can be written in the form of ${\sf{\dfrac{p}{q}}}$ where p and q are integers and q is not equal to zero. Such numbers are known to be rational numbers. For example ${\sf{\dfrac{1}{6}}}$ etc, but where q is not equal to zero! In ${\sf{\dfrac{p}{q}}}$ p is numerator and q is denominator.

All fractions are rational number but not all rational numbers are fraction!

• But why? Any Reason?

All fractions are rational number but not all rational numbers are fraction beacuse a fraction is that part of number that is always positive but rational numbers are those numbers which can be both positive and negative. That's all!

Symbol: Rational number is represented by the symbol Q. Rational came from word that is ratio and Q came from quotient. 'r' is a rational number.

Number system: The number system tell us about different type of numbers. For example as there are natural numbers, whole numbers, integers, rational numbers, irrational number.

• Kindly see attachment 3rd

• Green border means Natural numbers.

• Purple border means Whole numbers.

• Red border means integers

• Blue border means rational numbers.

a) Natural numbers: Symbol N is used to denote natural numbers. Natural numbers are those numbers which starts from 1 and last till infinity. ∞ is the symbol used to denote infinity.

b) Whole numbers: Symbol W is used to denote whole numbers. Whole numbers are those numbers which starts from 0 and last till infinity. ∞ is the symbol used to denote infinity.

c) Integers: Symbol Z is used to denote integers because Z cames from the German word that is zahlen that's mean to count. The set of whole numbers and negative of natural numbers known as integers. Integer can be negative or positive. Zero is neither positive nor negative integer!

• Refer to attachment 1st for integers number line.

On the number line, for example

• 2 > 1
• -1 > -2
• 2 > -1
• 0 > -2
• 2 > 0

Rational numbers on number line: On a number line postive numbers lines on the right hand side and the negative number lie on the left hand side.

• Refer to attachment 2nd for rational numbers, number line.

• If there are two negative rational number then the small one is greater than big one.

• Zero is always greater than negative number

• Zero is always smaller than positive number.