# Numbers and Numeral System

by Ron Kurtus (revised 8 June 2015)

A numeral system is a system of numbers used for counting and arithmetic. We normally use a system of numbers or numeral system that is based on 10—or decimal numerals—because we have 10 fingers for counting. Some ancient societies used system based on 12 or even 60. There is also a binary numeral system, based on the number two.

A number is a quantity that answers the question: "How many are there?"

Each number has its own name. Counting is putting the numbers in an order where the next number is one (1) more than the previous. For each number name, there is a symbol, which we consider the actual number.

Numbers listed in a sequence start from digit 0 and go through 9. Then they start at the next level.

Questions you may have include:

• How do we count?
• What are the number names and symbols?
• What is the decimal numeral system?

This lesson will answer those questions.

## Counting

Although it seems trivial, it is a good idea to look at counting to understand the number system and addition. Children start counting on their fingers: one, two, three, four, five, and so on. Each number in counting on your hand is one finger more than the previous.

Once you have established symbols for numbers, counting becomes easier, because you can then write it down.

## Names and symbols of numbers

Each number has a name and a symbol, which is the way the number is written.

### Roman numerals

In ancient Rome, they used Roman numerals as symbols for numbers. They would write down counting to ten as: I, II, III, IV, V, VI, VII, VIII, IX, X. Although it has some logic to it, it also is cumbersome and not convenient for such arithmetic operations like multiplying and dividing.

### Arabic numerals

The Arabic system of numbers or Hindu-Arabic numerals was more convenient for the various operations. Modernized versions of those numbers are the ones we use today.

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#### Symbol

zero 0 ten 10 twenty 20
one 1 eleven 11 twenty-one 21
two 2 twelve 12 twenty-two 22
three 3 thirteen 13 twenty-three 23
four 4 fourteen 14 twenty-four 24
five 5 fifteen 15 twenty-five 25
six 6 sixteen 16 twenty-six 26
seven 7 seventeen 17 twenty-seven 27
eight 8 eighteen 18 twenty-eight 28
nine 9 nineteen 19 twenty-nine 29

## Decimal numeral system

Most people use the decimal numeral or number system that is based on 10. The reason is because we have 10 fingers. When you count on your fingers, you start with one and continue until you have all ten fingers up. Then you start over with one finger up for 11.

### Names

The numbers 0 to 9 have unique names. The numbers from 10 to 19 have variations of the 0 to 9 names, including seven that are "teens". Afterwards, the names of the numbers seem pretty consistent. The number 20, is twenty, and 21 is twenty-one. Likewise, the number 30 is thirty, 31 is thirty-one, 32 is thirty-two, and so on.

Going on to the next level, 100 is one hundred, 101 is one hundred one, 123 is one hundred twenty three. 2305 is two thousand three hundred five.

Note: Although many people say "two thousand three hundred and five" the word and should not be used. It is reserved for indicating decimals. For example, 326.5 is three hundred twenty six and five-tenths.

The question is: why is ten designated as 10, when it represents all fingers up? Why isn't it like the Roman numeral X? Using 10 for ten and starting with 11 for eleven is what makes the Hindu-Arabic numerals so effective in mathematical operations.

### Binary numeral system

The binary numeral systems is used in computers, because electronic circuits can do rapid calculations using ON and OFF switches. They use 1 as ON and 0 as OFF. Counting from zero to eight in the binary system goes: 0, 1, 10, 11, 100, 101, 110, 111, 1000.

It is much easier for the computer circuits to use the binary system than the decimal system.

## Summary

A number is a quantity, and each number has its own name. Counting is putting the numbers in an order where the next number is one more than the previous. For each number name, there is a symbol or actual number. We use the decimal numeral system, which is based on 10, because we have 10 fingers for counting.

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## Resources and references

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### Websites

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numeral_system.htm

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