If you were to try to recite all the digits in the constant pi, you simply wouldn’t be able to because pi is an irrational number, or a number that “cannot be exactly expressed as the ratio of two integers,” according to AllAboutCircuits.com. It is the “the ratio of a perfect circle's circumference to its diameter.” An irrational number has an endless number of decimal places after the decimal. We need symbols, like ancient Greek letters, to stand for quantities we cannot physically write out with Arabic numerals.
We also use symbols to represent numbers we do not yet know. Algebra, calculus, trigonometry, statistics and other branches of mathematics use symbols to identify unknown values in equations. Any symbol, like a rectangle, can be used to stand for an unknown number, but letters are the most commonly used. Letters from the Greek alphabet as well as the Latin alphabet -- the alphabet used in the English language -- are widely used in mathematics.
The equation 6 + 7 = 13 can be written with symbols, for example. What if you did not know what number added to 6 equals 13? You could rewrite the equation as 6 + b = 13. In this example, the letter "b" stands for the number that, when added to 6, equals 13. To solve this equation, you would perform the opposite operation on both sides of the equation to get the b by itself. So subtracting six from both sides -- the opposite of addition -- you get b=7. You could use any symbol you like in an equation. The point is that it gives you a consistent way to manipulate the equation when you don't know all the numerical values.
If you go to the grocery store, and you have ten dollars to spend on mangoes that cost $1.25 each, how many can you buy? This is a very common type of simple math problem that you can write using symbols. This problem could be written as 1.25 x t = 10. That is, 1.25 times what number equals 10, or $1.25 for each mango times an unknown number of mangoes you can buy equals the maximum you can spend on mangoes, $10. To solve this problem, divide both sides of the equation by 1.25, and you find that t=8. You can purchase eight mangoes at $1.25 each.