The question that has perplexed those who studied and developed mathematical theorem throughout time is “How can nothing, as symbolized by zero, be something?”
The concept of zero seems to have originated around 520 AD with the Indian Aryabhata who used a symbol he called “kha” as a place holder. Brahmagupta, another Indian mathematician who lived in the 5th century, is credited for developing the Hindu-Arabic number system which included zero as an actual number in the system. Other mathematicians like al-Khwarizmi and Leonardo Fibonacci expanded the use of zero. By the Middle Ages, around the early 1200’s, this concept had come to Western society.
How important is zero? It is the number around which the negative numbers to its left stretch into infinity and the positive numbers to the right do likewise. It is neither positive nor negative. For that reason, zero is a pivotal point on thermometers and is the origin point for bathroom scales and the coordinate axis.
Zero is also important when you think of sets. An empty or null set is one which has no items in it.
Zero is so important that each of the mathematical operations has special rules called properties governing its use with other whole numbers.
The addition property of zero states that whenever zero is added to a whole number or vice versa the sum will be the whole number. Example: Ben had 3 apples and Sara had none. If they combined their apples, how many would there be in all?
The subtraction property of zero says that whenever zero is subtracted from a whole number, the difference will be the whole number, and whenever a whole number is subtracted from itself, the difference will be zero.
The multiplication property of zero is a little like the addition property in that it does not matter in what order you do the operation to the whole number. Thus, a whole number multiplied by zero equals zero, and vice versa.
The division property of zero is interesting. If zero is divided by a whole number, the quotient will be zero. This is the same as saying “divide zero into x number of groups and how many items will be in each group?” The answer, of course, is zero. You can not, however, divide a whole number by zero, because you can not come up with an inverse statement that makes sense. Can you divide x number of coins into groups of zero? Impossible! That is why mathematicians have a special term for x/0; they call it infinity.
Zero is very important for its place-holding value. If you have a number like two hundred four, how do you write it so that you understand that there are no tens in the number? You can not write it as 24 because that is a totally different number.
One neat thing when dealing with powers of ten: 10 squared=100. Notice the exponent 2 shows how many zeros will be in the written out form of the number. When you multiply two numbers which are powers of ten, the number of zeros in the answer equals the sum of the zeros in the factors. For example, 2000 multiplied by 300 equals 600,000, or 6 with 5 zeros after it.
When you round numbers like 6934 to the nearest ten, you place a zero in the ones place. 6934 rounded to the nearest ten equals 6930.
If you are writing a number with a decimal, you do not need to continue placing zeros to the right of the decimal. The decimal .033 (thirty-three thousandths) is still thirty-three thousandths if you write it .03300000. Why write all those extra zeros? But the zero in the tenths place is extremely important since it holds’ the tenths place by showing there are no tenths in the decimal.
Whether you call it zero, naught, or nil, zero has an important place in the field of mathematics.