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Explanation of Numbers and the Numeral System - Succeed in Arithmetic. Also refer to counting, symbol, Roman, Hindu, Arabic, decimal, binary, Ron Kurtus, School for Champions. Copyright © Restrictions

Numbers and the Numeral System

by Ron Kurtus (11 January 2008)

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 more than the previous. For each number name, there is a symbol, which we consider the actual number. We use the number or numeral system based on 10—or decimal numerals—because we have 10 fingers for counting.

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. There is a mini-quiz near the end of the lesson.

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 we have established symbols for numbers, counting becomes easier, because we 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. This has some logic to it, but it became 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.

Name

Symbol

Name

Symbol

Name

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.

Advantage of Hindu-Arabic numerals

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.

Answers to Readers' Questions

Make every action count

Resources

The following resources provide information on this subject:

Websites

Arithmetic Resources

Books

Top-rated Arithmetic books

Miscellaneous

Mini-quiz to check your understanding

1. Why do children count on their fingers?

Because they are ten fingers

It is an easy and logical way to count

Because they don't know how to use a calculator

2. What is the symbol or number for seven hundred twenty three?

Seven hundred twenty three

700 23

723

3. Why was the Roman numeral systems abandoned for the Hindu-Arabic system of numbers?

People became angry at the Romans for their high taxes

Roman numerals are difficult to use for addition and multiplication operations

No one really knows why the change to the Arabic numbers was made

If you got all three correct, you are on your way to becoming a Champion in Arithmetic. If you had problems, you had better look over the material again.

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