what is number system

8/7/2019 What is Number System

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Easier-A number system is a way of counting

things. It's a way of identifying the quantity ofsomething.

Harder A number system is the set of symbols

used to express quantities as the basis for

counting, determining order, comparing amounts,performing calculations, and representing value. It

is the set of characters and mathematical rules that

are used to represent a number. Examples include

the Arabic, Babylonian, Chinese, Egyptian, Greek,

Mayan, and Roman number systems. The ISBN


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Counting numbers are known as natural

numbers.

Thus, 1, 2, 3, 4, 5, 6, 7, ...,etc.,are all

natural numbers.


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All natural numbers together with 0 form the

collection of all whole numbers.

Thus, 1, 2, 3, 4, 5, 6, 7, ...,etc.,are all

whole numbers. Every natural number is a whole number.

0 is a whole number which is not a natural

number.


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All natural numbers, 0 and negatives of

natural numbers form the collection of all

integers.

Thus, ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4,5,...,etc., are all integers.

Every natural number is an integer.

Every whole number is an integer.


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A rational number is a number that can be

expressed as a fraction p/q where p and q

are integers and q0, are known as rational

number. 0 is a rational number, since we can write, 0

= 0/1

Every natural number is a rational number,

since we can write, 1=1/1, 2=2/1, 3=3/1,etc.

Every integer is a rational number.


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A rational number p/q is said to be in

simplest form, if p and q are integers having

no common factor other than 1 and q0.

Thus, the simplest form of each of 2/4, 3/6,4/8, 5/10, etc., is .


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Every rational number is expressible either as

a terminating decimal or as a repeating

decimal.

Every terminating decimal is a rationalnumber.

Every repeating decimal is a rational number.


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A number which can neither be expressed as

a termnating decimal nor as a repeating

decimal, is called an irrational numbers.

EXAMPLES OF IRRATIONAL NUMBERS

TYPE - I

Clearly, 0.01001000100001... is a

nonterminating and non repeating decimals

and therefore, it is irrational.


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TYPE II

If m is a positive interger which is not a

perfect square, then m is irrational.Thus 2, 3, 5, 6, 7, etc., are all

irrational numbers.

The Number : is a number whose exact

value is not 22/7.

In fact has a value which is

nonterminating and non repeating.

So, is irrational, while 22/7 is rational.


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Terminating Decimal

Every fraction p/q can be expressed as a

decimal.If the decimal expression of p/q

terminates, i.e., comes to an end, then thedecimal so obtained is called a terminating

decimal.

Examples

=0.25

5/8=0.625

2 &3/5=2.6


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A decimal in which a digit or a set of digits

repeats periodically, is called a repeating or

recurring decimal.

In a recurring decimal, we place a bar overthe first block of the repeating part and omit

the other repeating blocks.

Examples

2/3=0.666...=0.6

3/11=0.272727...=2.142857

11/6=1.8333...=1.83


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A number whose square is non-negative, is

called a real number.In fact, all rational and

all irrationalnumbers form the collection of

all real number. Every real number is either rational or

irrational.


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Closure property-The product of two real

numbers is always a real number.

Associative law- (a+b)+c=a+(b+c) for all real

numbers a, b, c.Commutative law- a+b=b+a for all real

numbers a & b.

Existence of Additive Identity-Clearly, 0 is a

real number such that 0+a=a+0=a for everyreal number a. 0 is called the additive

identity for real numbers.


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Existence of Additive Inverse-For each real

number a, there exists a real number(-a)

such that a+(-a)=(-a)+a=0.a and (-a) are called the additive inverse (or

negative) of each other.


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Closure Property-The product of two real

numbers is always a real number.

Associate Property- (ab)c=a(bc) for all real

numbers a, b, c.Commutative Law- ab=ba for all real

numbers a and b.


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Suppose we are given a number whose

denominator is irrational.Then, the process

of converting its denominator to a rational

number by multiplying its numerator anddenominator by a suitable number, is called

rationalisation.

what is number system

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