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model 1 basic number system
Basic number system questions answers practice test. Get trick & tips ...
model 2 divisibility, multiples, add and subtract based number system
Practice test for divisibility, multiples, addition & subtraction on number system ...
model 3 fraction of numbers
Aptitude number system finding fraction of numbers exam based questions ...
model 4 finding unit place of a number
New aptitude number system questions and answers for finding unit ...
model 5 smallest and largest fraction/numbers
New number system aptitude (Smallest Largest Fraction) multiple choice questions ...
model 6 operations of consecutive numbers (odd, even, square, etc.)
All new important number system aptitude Mcqs on finding consecutive ...
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number system Topic-wise Types, Definitions, Important fact & Techniques with Short Tricks & Tips useful for all competitive Examinations
Meaning & Definition of Number Systems:
A system in which we study different types of numbers, their relationship and rules govern in them is called number system. In the Hindu-Arabic system, we use the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. These symbols are called digits. Out of these ten digits, 0 is called an insignificant digit, whereas the others are called significant digits.
Numerals
A mathematical symbol representing a number in a systematic manner is called a numeral represented by a set of digits.
How to Write a Number?
To write a number, we put digits from right to left at the places designated as units, ten’s, hundred’s, thousand’s, ten thousand's, lakh’s, ten lakhs’, crore’s, ten crores’.
Let us see how the number 308761436 is denoted as,
It is read as "Thirty crore eighty-seven lakh sixty-one thousand four hundred thirty-six".
Face and Place Values of the Digits in a Number
Face Value
In a numeral, the face value of a digit is the value of the digit itself irrespective of its place in the numeral.
For example, In the numeral 486729, the face value of 8 is 8 the face value of 7 is 7, the face value of 6 is 6, the face value of 4 is 4 and so on.
Place (Local) Value
In a numeral, the place value of a digit changes according to the change of its place.
In a number,
- Place value of unit's digit = (Digit at one’s place) x10^{0}
- Place value of ten's digit = (Digit at ten's place) x10^{1}
- Place value of hundreds digit = (Digit at hundred’s place) x10^{2}
- Place value of thousand’s digit = (Digit at thousand’s place) x10^{3} and so on.
- The place value of number is also called the local value of the number.
For example, in the number 15683,
Place value of 5 | = Place value of thousand’s digit |
= (Digit at thousand’s place) x 10^{3} | |
= 5 x 10^{3} | |
= 5000 |
Types of Numbers
There are various types of numbers as follows,
1. Natural Numbers
Natural numbers are counting numbers and these are denoted by N,
i.e. N = {1,2,3……}
- All natural numbers are positive
- Zero is not a natural number, therefore 1 is the smallest natural number
2. Whole Numbers
All natural numbers and zero from the set of whole numbers and these are denoted by W,
i.e. W = {0, 1, 2, 3…..}
- Zero is the smallest whole number
- Whole numbers are also called as non-negative integers
3. Integers
Whole numbers and negative numbers form the set of integers and these denoted by I,
i.e. I = {……-4, -3, -2, -1, 0, 1, 2, 3, 4……}
Integers are of following two types
- Positive Integers
Natural numbers are called as positive integers and these are denoted by I^{+},
i.e. I^{+} = (1, 2, 3, 4….}
- Negative Integers
Negative of natural numbers are called as negative integers and these are denoted by I^{-}
i.e. I^{-} = (-1, -2, -3, -4,….}
“0 is neither +ve nor –ve integer”
4. Even Numbers
A counting number, which is divisible by 2, is called an even number.
For example, 2, 4, 6, 8, 10, 12…… etc.
- The unit's place of every even number will be 0, 2, 4, 6 or 8
5. Odd Numbers
A counting number, which is not divisible by 2, is known as an odd number.
For example, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19…… etc.
- The unit’s place of every odd number will be 1, 3, 5, 7 or 9
6. Prime Numbers
A counting number is called a prime number when it is exactly divisible by only 1 and itself.
For example, 2, 3, 5, 7, 11, 13. etc.
- 2 is the only even number which is prime.
- A prime number is always greater than 1.
- 1 is not a prime number; therefore, the lowest odd prime number is 3.
- Every prime number greater than 3 can be represented by 6n + 1, where n is integer.
How to test a number is prime or not?
If P given number, then
- Find the whole number x such that x >$√p$
- Take all the prime numbers less than or equal to x
- If none of these divides P exactly, then P is prime, otherwise P is non-prime.
For example Let P = 193, clearly 14 >$√193$
Prime numbers up to 14 are 2, 3, 5, 7, 11, 13.
No one of these divides 193 exactly.
Hence, 193 is a prime number.
7. Composite Numbers
Composite numbers are non-prime natural numbers. They must have at least one factor apart from 1 and itself.
For example, 4, 6, 8, 9, etc.
- Composite number can be both Odd & Even numbers.
- 1 is neither a prime nor a composite number.
8. Co-primes
Two natural numbers are said to be co-primes, if their common divisor is 1.
For example, (9, 8) (12, 16), etc.
- Co-prime numbers may or may not be prime.
- Every pair of consecutive numbers is co-prime.
9. Rational Numbers
A number that can be expressed in the form of p/q is called a rational number. Where, p and q are integers and q ≠ 0
For example $7/5,2/9,6/4,\text"13"/\text"19"$ etc.
10. Irrational Numbers
The numbers that cannot be expressed in the form of p/q, are called irrational numbers, where p, q are integers and q ≠ 0.
For example $√2, √3, √7, √\text"11",$ etc.
- π is an irrational number as $22/7$ is not the actual value of , but it is its nearest value.
- Non-periodic infinite decimal fractions are called irrational numbers.
11. Real Numbers
Real numbers include both rational and irrational numbers. They are denoted by R,
For example, $5/9, √2, √7, π, 3/7,$ etc.
Different types of questions or problems based on Number System, which are asked in various examinations:
- Model 1: Basic number system,
- Model 2: Divisibility, Multiples, Add and Subtract based number system,
- Model 3: Fraction of numbers,
- Model 4: Finding unit place of a number,
- Model 5: Smallest and Largest fraction/numbers,
- Model 6: sum of Consecutive numbers (Odd, even, etc.),
- Model 7: Ascending & descending order of numbers,
- Model 8: Using Simple BODMAS,
- Model 9: Dividend, Divisor, Quotient and Reminder, and
- Model 10: Find value of n & nth term.
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