Integers, Rational and Irrational Numbers-RRB
Integers and rational numbers
Natural numbers are all numbers N = (1, 2, 3, 4………..)
They are the numbers you usually count and they will continue on into infinity.
Whole numbers are all natural numbers including 0 e.g. W = (0, 1, 2, 3, 4……….)
Integers include all whole numbers and their negative counterpart e.g. I = or Z =(………-4, -3, -2, -1, 0,1, 2, 3, 4,………..)
All integers belong to the rational numbers.
A rational number is a number of the form p/q q≠0 (Q = p/q, q≠0)
Where p and q are both integers.
Example
The number 4 is an integer as well as a rational number. As it can be written without a decimal component it belongs to the integers. It is a rational number because it can be written as:
4/1 or 8/2 or −8/−2
Whereas
1/5=0.2 is a rational number but not an integer.
A rational number written in a decimal form can either be terminating as in:
1/5=0.2
Or repeating as in
5/6=0.83333…
All rational numbers belong to the real numbers.
If you look at a numeral line
You notice that all integers, as well as all rational numbers, are at a specific distance from 0. This distance between a number x and 0 is called a number’s absolute value. It is shown with the symbol|x|
If two numbers are at the same distance from 0 as in the case of 10 and -10 they are called opposites. Opposites have the same absolute value since they are both at the same distance from 0.
|10|=10=|−10|
Irrational Numbers
Irrational Numbers sqrt(2) i.e √2, pi, i.e π =3.142….., e, i.e = 2.718….the Golden Ratio …
Irrational numbers are numbers that can be written as decimals but not as fractions.
Irrational numbers Q′ =(Numbers which are not irrational i.e it can not be written in the form p/q, q≠0)
An irrational number is any real number that is not rational.
Real number is a number may be a natural number, a whole number, integer, rational number or irrational number.
(that we can take of in this world, we define R = ( -∞, ∞)
A real number is a number that is somewhere on a number line, so any number on a number line that isn’t a rational number is irrational. The square root of 2 is an irrational number because it can’t be written as a ratio of two integers.
Other irrational numbers include the square root of 3, the square root of 5, pi, e, and the golden ratio. ( Pi = 3.14159… and e = 2.71828…, )
Pi is an irrational number because it cannot be expressed as a ratio (fraction) of two integers: it has no exact decimal equivalent, although 3.1415926 is good enough for many applications. The square root of 2 is another irrational number that cannot be written as a fraction.
Complex Number is one with square roots of negative numbers, such a number is called complex.
Ex- i =√-1,
5i, 2+3i, 9 – 7i, -1-89i………….