A project on Developed of Number system and their needs
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Answer:
The number system is a mathematical notation which is used to represent numbers of a given set. The number system with which we are most familiar is the decimal (base-10) system. It is also known as system of numeration or numeral systems which helps us to express numbers using digits or other symbols.
Basically, the number system represents a meaningful set of numbers including integers , rational numbers. Each and every no. shows the algebraic and arithmetic numbers.
In ancient times, various systems for number system were used such as the ancient Egyptians, the ancient Babylonians.
But , now - a -days, the Decimal Number System is used.
For example: 123.
This shows three numerals : 1,2,3. Because we use a place value system, which shows , 1 is 100, 2 is 20 and 3 is 3 as it stands in the ones place.
So, instead of writing 100+20+3, we write 123
Types of Number System:
a) Natural Numbers: Natural numbers are the numbers 1, 2, 3, ...
b) Integers: All natural numbers are integers including 0, -1, -2, ...
c) Rational numbers: These are fractions p/q where q is non-zero and p and q are both integer.
For example, all integers are rational (pick q =1).
d) Real numbers: Real numbers are all numbers that can be written as a possibly never repeating decimal fraction.
e) Complex numbers: These are numbers in form of
z = a+ bi, where a and b are real numbers and i (called the imaginary unit)is the square root of negative 1, i.e.,
t^2 = -1
f) Algebraic numbers:These are complex numbers that can be obtained as the root of a polynomial with integer
coefficients.
For example, rational numbers are algebraic, and so are roots of integers.
g) Transcendental numbers: These numbers are real numbers. For example e and π are transcendental (and real).
Properties of Numbers:
1) Associative Property:
In case of addition : a+(b+c)=(a+b)+c
In case of multiplication: a.(b.c)=(a.b).c
2) Commutative Property:
In case of addition : a+b=b+a
In case of multiplication: a.b=b.a
3) Inverse Property:
In case of addition : a+(-a)=0
In case of multiplication: a.(1/a)=1
4) Distributive Property:
a.(b+c)=a.b+a.c
Step-by-step explanation:
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The number system is a procedure of representing numbers of a set in a systematic manner. The most commonly used system of numerals is decimal number system.
Let's get into the history of origin of number system in the world.
Aryabhatta, one of the greatest mathematecian of history, developed the system of place value notation in 5th century and later Brahmagupta developed the symbol of zero. The system became prominent and started spreading slowly all over the world as a common system for notation of numbers in a set.
There are three main types of number
- real numbers
- imaginary numbers
- complex numbers
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