Countless Ways to Count

These are all symbols that people of different cultures and times used to represent numbers. A set of symbols used to represent quantities is called a "number system."

About 5,000 years ago, the Egyptians developed a writing system called hieroglyphics, or picture writing. They used pictures for words, and pictures for numbers. Using this system, the number 12,423 used one "10 thousand" symbol, two "thousand" symbols, four "hundred" symbols, two "ten" symbols, and three "one" symbols. It looked like this:

At about the same time the Egyptians were writing these number symbols, the Maya Indians of Central America used bars, dots, and a clam shape to show numbers:

To them, the number 19 looked like this:

You might recognize another number system that is still used in some places today: Roman numerals. These began to be used by the Romans about 500 BC.

In this system, the number 157 is written CLVII.

At first, numbers like 9 and 40 were written like this: 9 was VIIII, 40 was written XXXX. Then a shortcut developed. If a smaller number is written before a larger number, you subtract it. So XI is 11 (10 plus 1), and IX is nine (10 minus 1). VI is six (5 plus 1), and IV is four (5 minus 1). Using this system, the year 1997 is written this way: MCMXCVII.

In all these number systems, you have to count up symbols and add or subtract just to figure out what the number is. Math was very simple in those days, since numbers were so complicated just to write and read.

Do you notice something missing from the Egyptian and Roman systems?

There's no zero. These systems didn't have much need for a zero. If you had nothing, you just didn't write about it. The zero became more important with a number system that used "place value."

Place value means that where each symbol is placed in the number is important. The Mayans had a well-developed place-value number system, though they used it more for calendars than for calculations.

In about 300 BC, Hindu mathematicians in India used a system that had nine symbols for the numbers 1 to 9. The symbol's position in the number showed if it meant ones, tens, hundreds, or more. The number 572 meant five hundreds, seven tens, and two ones.

Place wasn't important in the Egyptian system. The number

would be the same if it were written

But in the Hindu system, 572 is a different number from 275, because this system uses position to show value.

What happened if someone using this system had hundreds and ones, but no tens? The symbol for 307 was written 3 7, with a space between the two numerals. The blank space was to show that there were no tens in the number. But if you write the symbols too closely together, it could be mistaken for 37.

Writers began to put a dot between the numbers to show the empty space. Eventually, the dot grew into a circle and became the symbol for nothing, or zero: 307. ("Zero" is from the Arabic sifr.)

The idea of zero seems pretty obvious to us today. But it is one of the most important inventions in early arithmetic. Just as the wheel is a simple idea with many uses, the zero gave mathematicians new ways to think about numbers. It let people explore many new and complicated mathematical ideas.

The Arabs picked up this Indian number system, changing the symbols a little but using the ideas of place value and zero. From there, the system spread to Europe. Now it is commonly used around the world, and its symbols are called Arabic numerals.

You may or may not be excited about your next math test, but you certainly have something to be grateful for: You don't have to write your answers in hieroglyphics.

Design Your Own Number System

Poeple have always counted on their fingers. But some people count on their heads, too. In parts of China, the word for "two" is the same as the word for "eyes." In other languages, the word for "five" is the same as the word for "hand," because a hand has five fingers.

Some ancient native American pictures drawn on rock walls show a handprint next to a horse to mean "five horses."

Many counting systems are based on the number 10. Can you think of a reason why 10 is so popular?*

Suppose you made a number system using hieroglyphics, or pictures, to show the numbers 1 to 9. Many number systems use a single line to mean "one." The symbol for "two" might be a simple drawing of eyes or ears. "Five" might look like a hand.

See if you can think of symbols for all the numbers, based on objects that remind you of the number.

An example might be the number of petals on a certain flower or legs on a chair. Remember to keep the symbols simple, so they can be written quickly and clearly. Can you think of a symbol for zero?

*People often used their fingers to count. Since they had 10 fingers, they thought about numbers in terms of 10.