NUMBERS - CONTENT

 Types of Numbers

NATURAL NUMBERS

The natural numbers are the ordinary numbers, 1, 2, 3,. . . with which humans count. It is denoted by the letter N.

WHOLE NUMBERS

Natural numbers together with 0 form the set of whole numbers. It is denoted by the letter W.

i.e. 0 , 1, 2, 3, 4…  are whole numbers.

EVEN NUMBERS

Numbers divisible by 2 form the set of even numbers.

i.e. 0 , 2 , 4, 6, 8, …. are even numbers

ODD NUMBERS

Numbers which are not even form the set of odd numbers

i.e. 1, 3, 5, ,7, 9 …. are odd numbers.

PRIME NUMBERS

A number is said to be prime if the only factors are 1 and the number itself.

i.e  2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37…… are primes.

COMPOSITE NUMBERS

A number is said to be composite if it has more than two factors.

In other words, numbers that are not prime are said to be composite. A number except 1 cannot be both prime and composite.

1 is neither prime nor composite.

i.e. 4, 6, 8, 9, 10, 12, 14, 15…..are composite numbers.

NUMBER LINE

A straight line on which equally spaced points/segments are marked is called a number line. 

PLACE VALUE

Place value is the value of each digit in a number

For example, consider the number 7546938. The place value of each digit is given in the chart below.

Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
7	5	4	6	9	3	8

INTEGERS

The numbers which have a direction and a size are called integers. If a direction is chosen as positive (+), then the opposite direction is taken to be negative (- ). For example, if profit is considered as a positive (+) number, then loss will be negative (-).

On a number line, the positive numbers are to the right of zero and the negative numbers are to the left of zero.

Rules for Addition	Rules for Multiplication	Rules for Division
·        (+ve) + (+ve) = +ve Ø  i.e 2+3 = 5 ·        (-ve) + (-ve) = -ve Ø  i.e. -5+-7 = -12 ·        To find the sum  of (+ve) and (-ve) first subtract the numbers and then put the sign of the greater number. Ø  -16 + 8 = -8 Ø  17 + -6 = 11	·        (+ve) X (+ve) = +ve Ø  i.e. 7 x 4 = 28 ·        (-ve) X (-ve) = +ve Ø  -9 X -3 = 27 ·        (+ve) X (-ve) = -ve Ø  4 x -2 = -8 ·        (-ve) X (+ve) = -ve Ø  -5 x 6 = -30	·        (+ve) / (+ve) = +ve Ø  i.e. 112 / 4 = 28 ·        (-ve) / (-ve) = +ve Ø  -9 / -3 = 3 ·        (+ve) / (-ve) = -ve Ø  4 /-2 = -2 ·        (-ve) / (+ve) = -ve Ø  -180 / 6 = -30

PERFECT NUMBERS

Perfect number is a positive integer that is equal to the sum of its proper divisors.

Smallest perfect number is 6, which is the sum of 1, 2, and 3.

Other perfect numbers are 28, 496, and 8,128.

RATIONAL NUMBER

A rational number is a number such as -3/7 that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

Every integer is a rational number: for example, 5 = 5/1

IRRATIONAL NUMBER

An Irrational Number is a real number that cannot be written as a simple fraction. The irrational number means not a Rational number.

REAL NUMBERS

Real numbers are the numbers that include both rational and irrational numbers.

 

COMPLEX NUMBERS

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i represents the imaginary unit, satisfying the equation i² = −1. Because no real number satisfies this equation, i is called an imaginary number.

ABSOLUTE VALUE OF A NUMBER

The absolute value of a number is the distance of that number from zero on the number line. The absolute value of x is denoted as | x | and read as "the absolute value of x". This means that | 4 | = 4, because 4 is four units to the right of zero, and also | –4 | = 4, because –4 is four units to the left of zero.

ROMAN NUMBER

Roman numerals are a system of numerical notations used by the Romans.

The symbols are I, V,X, L, C, D, and M.

S	V	X	L	C	D	M
1	5	10	50	100	500	1000

DIVISIBILITY TEST

A number is divisible by 2 if the last digit of the number is 0, 2, 4, 6, or 8.

A number is divisible by 3 if the sum of the digits is divisible by 3.

A number is divisible by 4 is that if the number formed by the last two digits in a number is divisible by 4.

A number is divisible by 5 if the last number is either 0 or 5.

A number is divisible by 6 if it is divisible by 2 and 3 both.

To check whether a number is divisible by 7 take the last digit of the number, double it .Then subtract the result from the rest of the number If the resulting number is a multiple of 7 then the given number is also divisible by 7.

A number is divisible by 8 if the last three digits of a whole number are divisible by 8.

A number is divisible by 9 if the sum of the digits is divisible by 9.

A number is divisible by 10 if the last digit is 0.

A number is multiple of 11, if the difference of the alternating sum of digits is a multiple of 11 .(e.g. 1221 is divisible by 11 because 1-2+2-1 = 0, which is a multiple of 11)