Numbering Systems, a Historical View

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1.1Numbering Systems, a Historical View


In these revision notes for Numbering Systems, a Historical View, we cover the following key points:

  • What are numbers? Where did humans begin using them?
  • What are the numbering systems ancient civilizations used to count things?
  • What are the symbols used to represent numbers in each of the numbering systems?
  • What are the two numbering systems in use today? What are they mostly used for?
  • How to convert numbers from one system into another?
  • How to express big numbers as Roman numerals?

Numbering Systems, a Historical View Revision Notes

In antiquity, people were not aware of numbers but developments in interpersonal relationship meant that people needed a means of identifying small amounts of objects around and compare them. Ancient populations invented signs and symbols to represent numbers.

Numbers are mathematical objects used to count, measure and label things.

Egyptians, as one of the oldest civilizations on Earth, used a vertical line to represent ones and an inverted U-symbol to represent tens. Babylonians used two other symbols, namely a triangle to represent ones and a kind of kite symbol to represent tens. Mayans used horizontal bars to represent fives and dots for ones. All these numbering systems have stopped being used over time.

Romans had a more advanced system of numerals. They use the symbol I to represent ones, V for five, X for tens, L for fifty, C for hundreds, D for five hundred and M for thousands. A horizontal line placed above the number increases its value by 1000 times.

The Hindu-Arabic system contains numerals we actually use in all modern activities. The Hindu-Arabic is a numbering system containing 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (hence the name decimal system). The value of these digits increases by 10 times when moving one position to the left. The rightmost digit of a Hindu-Arabic number shows the units (ones), then the next digit shows tens, then hundreds, and so on.

To simplify understanding, numbers are grouped into sets of three digits that start from right to left. These groups are known as classes. Thus, starting from the left we have the simple class, the thousands class, the millions class, billions class and so on. A small space or a comma is often used to separate the classes from each other. The three digits contained in a class are known as placeholders. Thus, for each class we have the placeholder of ones, tens and hundreds.

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