Numbers play an important role of in mathematics:
Numbers / Properties / Types of number
A digit is any one of these symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
For example, the number 43 is written with two digits, 4 and 3.
Example: The numeral 9 is made up of 1 digit ("9").]
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Comparison of numbers:
Rule I: A number with more digits is always greater than a number with less digits.
Example: Compare 598 and 98.
598 has 3 digit while 98 has 2 digits.
So, 598 is greater than 98.
598 > 98
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Rule II: When the digits of two numbers are the same, we start comparing the digits from the left side until we come to the unequal digits. Example:
Compare 379 and 279.
3 > 2
so, 379 > 279.
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If hundred place digit is equal of the given two numbers then tens place digit will be compared.Example:-
Compare 586 and 567.
5 = 5
8 > 6
Hence, 586 > 567
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Natural numbers & whole numbers
Natural numbers are also called counting numbers and All natural number along with 0 are called whole numbers .
[ 1, 2, 3, 4....etc are all natural numbers.]
[ 0, 1, 2, 3, 4, 5.. etc are whole numbers.]
[ Natural number is denoted by the letter N.]
[ The set of whole numbers is denoted by the letter W. ]
[ The smallest natural number is 1 and whole number is 0.]-
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Properties of Natural numbers
* Even number: The number which are divisible by 2 are called even number. 0, 2, 4, 6, 8....etc are even numbers.
* Odd number: The number which are not divisible by 2 are called odd numbers. 1, 3, 5, 7, 9, 11, 13, 15, 17... etc are odd numbers.
Property of even number:
When we add (subtract / multiply) even or even numbers the results are alalways:
Even + Even = Even (2+4=6)
Even - Even = Even (4 -2=2)
Even × Even = Even (2×4=8)
Property of odd number:
When we add (subtract / multiply) odd or odd numbers the results are always:
Odd + Odd = Even (3+5=8)
Odd - Odd = Even (5 - 3=2)
Odd × Odd = Odd (3×3=9)
Properties of even and odd numbers:-
When we add (subtract / multiply) even or odd numbers the results are always:
Even + Odd = Odd (2 + 3 = 5)
Odd + Even = Odd (4 + 5 = 9)
Odd - Even = Odd (5 - 2 = 3 )
Even - Odd = Odd (4 - 3 = 1 )
Odd × Even = Even (3 × 2 = 6)
Even × Odd = Even (4 × 5=20)
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When we divide even / odd numbers the results are always:
*Even number is divisible by 2, and leaves the remainder 0.
*An odd number is not completely divisible by 2, and leaves the remainder 1.
*An even number ends with 0, 2, 4, 6, and 8
*An odd number ends with 1, 3, 5, 7, and 9
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Types of number
1.Natural number 2.Whole number. 3.Integer number 4.Rational number 5.Irrational number
1. Natural number:-
Natural numbers are also called counting numbers.
[ 1,2,3,4..etc are all natural numbers.]
[ It is denoted by the letter N.]
[ The smallest natural number is 1.]
2. Whole number:-
All natural number along with 0 are called whole numbers .
[ 0, 1, 2, 3, 4, 5..... etc are whole numbers.]
[ The set of whole numbers is denoted by the letter W. ]
[ The smallest whole number is 0.]
3. Integer number:
The whole numbers together with the negatives of counting or natural number are known as integers.
[The set of integers is denoted by the letter l.
-3,-2,-1, 0,1,2,3...... etc. are all integers.
1,2,3,4........ etc.are positive integers.
-1,-2,-3,-4,....... etc. are negative integers.
0 is neither positive nor negative.]
4. Rational number:
A number of the form p/q, where p and q are integers and p≠0, is called a rational number.
[ p is called the numerator and q is called the denominator of the rational number.
Thus, every rational number is the quotient of two integers such that the denominator is non-zero.]
[ the set of rational number is denoted by the letter Q.]
For examples: 1/2, -3/-4, x/y etc.
*Any number which can be express as p/q form.
5. Irrational number:
Number which when expressed in decimal form are expressible neither in terminating nor in repeating decimals are known as irrational numbers.
[ The symbol used to represent the irrational symbol is “P”]
[ A ]. Questions:- * Give the answer the followings : 1. The smallest even number. 2. The smallest odd number. 3. The first five even numbers. 4. The first five odd numbers. 5. The last five two-digit even numbers. 6. The last five two-digit odd numbers. 7. Write the even numbers coming between 15 and 25. 8. Write the odd numbers coming between 98 and 108. 9. Write the even number coming just before19. 10. Write the odd number coming just after 72. 11. Write the greatest odd number of one digit. 12. Write the smallest even number of two digits. 13. Write the greatest odd number of two digits. 14. Write the smallest even number of three digits. 15. Write the first even number between 41 and 49. 16. Write the last odd number between 88 and 100. 17. Find whether the number is even or odd: a. 458. b. 2983. c. 8661. d. 33570. --------------------------*-----------------------. [A]. Answers:- 1. The smallest even number. Ans: 2 2. The smallest odd number. Ans: 1 3. The first five even numbers. Ans: 2, 4, 6, 8, 10. 4. The first five odd numbers. Ans: 1, 3, 5, 7,9. 5. The last five two-digit even numbers. Ans: 90, 92, 94, 96, 98. 6. The last five two-digit odd numbers. Ans: 91, 93, 95, 97, 99. 7. Write the even numbers coming between 15 and 25. Ans: 16, 18, 20, 22, 24. 8. Write the odd numbers coming between 98 and 108. Ans: 99, 101, 103, 105, 107. 9. Write the even number coming just before19. Ans: 18 10. Write the odd number coming just after 72. Ans: 73. 11. Write the greatest odd number of one digit. Ans: 9. 12. Write the smallest even number of twod digits. Ans: 10. 13. Write the greatest odd number of two digits. Ans: 99. 14. Write the smallest even number of three digits. Ans: 100. 15. Write the first even number between 41 and 49. Ans: 42. 16. Write the last odd number between 88 and 100. Ans: 99. 17. Find whether the number is even or odd: a. 458. Even. b. 2983. Odd. c. 8661. Odd. d. 33570. Even. --------------------------*-----------------------.