Real Numbers
A combined set of rational numbers and irrational numbers
, is called the set of Real numbers.
What is a real number?
By definition, a number that can be plotted on a number line is called a real number. A real number is either a rational or an irrational number. Thus, the real number 2 is a rational number, while the real number 2 is an irrational number. A real number can be thought of a point on an infinitely long number line, where in the integers are equally spaced. And any point on that line would represent a real number.
I like to share this
Fraction to Percent Calculator with you all through my article.
Properties of the real number system:
1. Closure: Real numbers are closed under addition and multiplication. That means a+b = real number and a*b = real number.
2. Commutative: For real numbers a and b, a+b = b+a and a*b = b*a.
3. Associative: For real numbers a and b , (a+b)+c = a+(b+c) and (a*b)*c = a*(b*c)
4. Identity: In addition, a+0 = 0+a = a i.e., 0 is the identity element for the operation of addition. In multiplication, 1*a = a*1 = a i.e., 1 is the identity element for the operation of multiplication.
5. Inverse: For each a, there is a unique real number (-a), called the additive inverse of a such that a+(-a) = (-a)+a = 0. For each a " 0, there is a real number 1/a, called the multiplicative inverse of a such that a * (1/a) = (1/a) *a = 1.
6. Distributive: a*(b+c) = ab + ac and (b+c)*a = ba + ca
7. Order: The real number system is ordered, i.e., if a and b are different real numbers, then either a b.
8. Density: The real number system is dense, that is, between any two distinct real numbers there are infinitely many more real numbers.
9. Completeness: The real number system is complete.
Adding real numbers or subtracting real numbers:
When adding or subtracting real numbers, the rational parts are added and the like irrational parts are combined. Everything else is left as it is. For example: 1+2+3"(2) +"5 = 1 + 4"(2) +"5
Example: Width of a field is 2 less than its length. If length = "10 then find the perimeter.
Solution: Length = "10, therefore width = "10 "" 2.
So perimeter = P = 2(Length + Width)
P = 2("10 + "10-2)
P = 2(2"10 "" 2)
P = 4"10 " 4 ------------- Answer.
by: Omkar Nayak
Common Types Of Industrial Valves How To Use A Bench Press Shirt Obtain Actuarial Certificate In Record Time Of Twenty Minutes Pacifica Aurum : Living In Aurum Enjoy All Year Round By Installing Folding Doors To Conservatory Extensions Virgo (kanya) By Hemant Sharma Astrologer Tips On Sealing Your Deck Demands Following The Trends Of The Market Retirement Communities: Visit There Someday Diaper Rash Cream Is The Secret To Happy Babies Eyeglasses St Louis: To See Better Descubre Menorca Con Tu Coche De Alquiler What Are Wire Mesh Products