General

# What Are Roman Numerals?

Roman numerals are the symbolic representation of numbers using an alphabet or combination of alphabets. The system has derived its name from ancient Romans who introduced this technique for counting activities in trade and communication.

In this system, the alphabets I, V, X, L, C, D, and M are used to express different numbers. The alphabets and corresponding numbers are given below.

I = 1, V = 5, X = 10, L = 50, C = 100, D = 500 and M = 1000.

A number can be decomposed to express it as a Roman numeral.

For Example, 3 = (1+1+1) = III, 6 = (5 +1) = VI, 15 = (10+5) = XV etc.

Roman numerals follow an additive pattern for expressing numbers. A letter placed after a letter of equal or greater value means the addition of both values. For example, XVII = 17 and CL = 150. But there are restrictions as well. A particular letter can’t be used more than three times consecutively. For example, it is not permissible to use the same four letters to represent 4, 45, 9, 90 as IIII, XXXXV, VIIII, LXXXX, respectively. Alternatively, such numbers are denoted by using symbols that indicate subtraction. The rule says that a letter placed before another letter of the greater value indicates its subtraction from the greater value digit. For example 4 = IV, VL = 45, 9 = IX and 90 = XC.

# Real Numbers

All those numbers that can be found in reality are real numbers. Real numbers can be placed on the number line and used for all arithmetic calculations. The set of real numbers includes the five types of numbers as described below.

1. Natural numbers: All positive counting numbers (such as 1, 2, 7, 34.. etc.)
2. Whole numbers: All natural numbers including zero (such as 0, 1, 2, 3,.. etc. )
3. Integers: All positive counting numbers, negatives of counting numbers, and zero (such as 0, 4, -21, -56.. etc.)
4. Rational numbers: The numbers that can be expressed as a ratio of two integers and the denominator is not equal to zero. (such as 8, 0, 2/3, -6, 3.5.. etc.)
5. Irrational numbers: the numbers that can’t be denoted as a ratio of two integers or don’t have a finite value (such as 1/3, 22/7.. etc.)

So it can be said that all rational numbers (like positive and negative integers and fractions) and irrational numbers constitute the set of real numbers. Any real number has to be either a rational or an irrational number. In other words, if we choose any number from the set of real numbers, it can be either a rational or irrational number.

## Real Numbers Properties

There are four main properties of real numbers that are useful in any mathematical calculation. These are as follows:

Commutative property:

For two real numbers a and b, the general form will be a + b = b + a for addition and a x b = b x a for multiplication.

Associative property:

If a, b and c are three real numbers, then for addition, the general expression will be a + (b + c) = (a + b) + c and for multiplication the general expression will be (a x b) x c = a x (b x c)

Distributive property:

For three real numbers a, b and c, this property states that a x (b + c) = a x b + a x c and (a + b) x c = a x c + b x c

Identity property:

If a is a real number, then a + 0 = a (here 0 is the additive identity) and a x 1 = a ( here 1 is the multiplicative identity). There are many other interesting Maths concepts presented in an interesting way at Cuemath. Visit the website and explore more.