In Mathematics all calculation is the game of numbers. Today we'll know about basic definitions which are related to Decimal Number System.
We'll learn about these definitions.
1. Decimal Number System
2. Digits
3. Number
4. Natural Numbers
5. Whole Numbers
6. Integers
7. Fraction
8. Decimal Numbers
9. Rational Numbers
10. Irrational Numbers
11. Real Numbers
Definitions:
Q. What is Digit?
Ans. Digits : Digit is the basic unit of Mathematics. There are 10 digits in decimal number system as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Q. What is Number?
Ans. Numbers : The combination of digits is called number.
Examples - 1, 2, 45, 1025 etc.
Q. What is Decimal Number System?
Ans. Decimal Number System : The number system in which there are 10 digits. In Decimal Number System there are 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
• We use decimal number system for calculation of mathematics.
Types of Numbers -
Q. What is Natural Number?
Ans. Natural Numbers : Counting numbers 1, 2, 3, 4, .............. are called natural numbers.
• Smallest natural number is 1.
• Greatest natural number is not defined.
Q. What is Whole Number?
Ans. Whole Numbers : All Natural numbers together with 0 are called whole numbers.
Numbers 0, 1, 2, 3, 4, 5, ................. are whole numbers.
• Smallest whole number is 0.
• Greatest whole number is not defined.
• All natural numbers are whole numbers.
• But all whole numbers are not natural numbers.
Q. What are Integers?
Ans. Integers : All natural numbers with 0 and negatives of natural numbers are called integers.
Numbers ................ -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ............... are integers.
There are two types of integers.
Positive Integers : 1, 2, 3, 4, 5, ............ are positive integers.
Negative Integers : -1, -2, -3, -4, -5, .............. are negative integers.
Zero : 0 is neither positive integer nor negative integer.
• All natural numbers are integers.
• All whole numbers are integers.
• But all integers are not natural or whole numbers.
Q. What is Fraction?
Ans. Fraction : Numbers in the form of p/q where p and q are whole numbers and q should not be zero.
In p/q , p is numerator and q is denominator.
There are 3 types of fractions.
Proper Fraction : A fraction in which numerator < denominator
Improper Fraction : A fraction in which numerator > denominator
Mixed Fraction : A combination of whole number and proper fraction.
• Fractions are always positive.
Q. What is Rational Number?
Ans. Rational Numbers : Numbers in the form of p/q where p and q are integers and q should not be zero are called rational numbers.
There are two types of rational numbers.
Positive Rational Numbers : Rational numbers with same signs of numerator and denominator.
Negative Rational Numbers : Rational numbers with different signs of numerator and denominator.
Zero : Zero is neither positive nor negative rational number.
• All natural numbers are rational numbers.
• All whole numbers are rational numbers.
• All integers are rational numbers.
• All fractions are rational numbers.
• But all rational numbers are not natural or whole or integers or fractions.
Irrational Numbers : Numbers which can not be written in the form of p/q are called irrational numbers.
Real Numbers : All rational numbers and irrational numbers together are called real numbers.
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