Numbers can be represented in different ways. A number is an idea or quantity, a symbol is a mark used to represent something, and a numeral is a symbol or group of symbols that represents a number.
Egyptian numerals
Egyptian numerals were built around groups of ten. Different symbols represented units, tens, hundreds, thousands and larger powers of ten. To write a number in this system, symbols are repeated or combined to show the required quantities.
For example, a representation of 25 would contain two symbols for tens and five symbols for units. A representation of 300 would contain three symbols for hundreds. When working with Egyptian numerals, count the value of each symbol and add the values together.
Roman numerals
Roman numerals use letters to represent values. The most common symbols are shown below.
| Symbol | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1,000 |
When a smaller numeral is written after a larger numeral, the values are added. For example, VI = 5 + 1 = 6. When a smaller numeral is written before a larger numeral, the smaller value is subtracted. For example, IV = 5 − 1 = 4.
Examples include IX = 9, XI = 11, XV = 15, XL = 40, and XC = 90.
Arabic numerals
The symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are called Arabic numerals. Our ordinary system of writing numbers is based on groups of ten, so it is called a decimal place-value system.
| Digit | Name |
|---|---|
| 0 | Zero |
| 1 | One |
| 2 | Two |
| 3 | Three |
| 4 | Four |
| 5 | Five |
| 6 | Six |
| 7 | Seven |
| 8 | Eight |
| 9 | Nine |
The value of a digit depends on its position. In 4,938, the digit 4 is in the thousands place, 9 is in the hundreds place, 3 is in the tens place, and 8 is in the units place. Therefore, the value of 4 is 4,000.
Worked examples
- In 45, the value of 4 is 40.
- In 468, the value of 4 is 400.
- In 4,938, the value of 4 is 4,000.
- In 3,456,548, the value of 3 is 3,000,000.
Summary
- A number represents a quantity or idea.
- A numeral is a symbol or group of symbols representing a number.
- Egyptian numerals are based on repeated symbols for powers of ten.
- Roman numerals use letters and follow addition and subtraction rules according to position.
- Arabic numerals use the ten digits from 0 to 9 and depend on place value.
Practice questions
- Write 20, 25, 300 and 175 using Egyptian numeral symbols.
- Write 4, 19, 55, 302 and 2,349 in Roman numerals.
- State the value of the underlined digit in five numbers of your choice.
- Write the Arabic numerals from zero to nine in words.
Note: In written mathematics, always check the order of Roman-numeral symbols and the place value of every digit in an Arabic numeral.
