What is a number?

A number is a count or measurement that is really an idea in our minds.

We write or talk about numbers using numerals such as "4" or "four". But we could also hold up 4 fingers, or tap the ground 4 times. These are all different ways of referring to the same number.

What is a numeral?

A numeral is a symbol or name that stands for a number.


Example: 3, 49, and twelve are all numerals.


So the number is an idea, the numeral is how we write it.

What is a digit?

A digit is a single symbol used to make numerals.

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the ten digits we use in everyday numerals.

The value of a digit is understood through its position in place value.

As a digit's place value moves more to the left in this chart its value increases. A 9 may be a larger digit than a 1, but if the 9 is in the ones place and the 1 is in the tens place the 1 will have a greater value.

1

9

​1 ten = 10 ones

9 ones = 9 ones

As we move from the ones place the value increases by ten times for each place to the left you move.

A 5 in the ones place has a value of 5. A 5 in the tens place has a value of 50 (50 ones). A 5 in the hundreds place has a value of 500 (500 ones).

4

5

3

2

1

We can represent numbers in different ways.

Standard Form: This is the normal way we are used to seeing numbers.

ex. 15
489 654
2 540 651

We can represent numbers in different ways.

Word Form: Using words to represent numbers.

ex. 15 = fifteen
489 654 = Four hundred eighty-nine
thousand six hundred fifty-four

We can represent numbers in different ways.

Expanded Form: Adding the value of each place value spot together.

ex. 15 = 10 + 5
489 654 = 400 000 + 80 000 + 9000 + 600 +50 + 4

​Each counter in this place value chart adds value to the number being represented.

We can express this value as a numeral: 39 057

What is an expression?

Numbers, symbols and operators (such as + and ×) grouped together that show the value of something.

Example:
• 2 + 3 is an expression

Note: an expression does not have an equals sign.

What is an expression?

12 + 5 is an addition expression equivalent to 17.

10 - 3 is a subtraction expression equivalent to 7.

4521 + 12 521 is an addition expression equivalent to 17 042.