Numbers

This is little Lucy. She loves to play with a ball. But she doesn't really have a ball at the moment - she's thinking of the ball, so she has the idea of a ball in her mind. In fact, she has the idea of one ball in her mind, and she wants to chase it!

Numbers are ideas too. They're the ideas we use to count things or measure them. We might count Lucy's ball with the number one, but it is really just an idea in our minds.

If we want to talk or write about numbers, rather than just thinking of them, we need to use numerals such as "1" or "one". But we could also hold up 1 finger, or tap on the ground with our foot once in the same way that some dogs have been trained to "count". Lucy might thump her tail against the couch once if she was as clever as we like to pretend she is.

There are many different ways of referring to the same number. All numbers have names or symbols that we call numerals. Some numbers like \(\pi\) ("Pi") can't be written down exactly in decimal format, but we still have the idea of what "Pi" means, so it is still a number.

Just like words are made up of letters, digits are the symbols that make up numerals.

Our everyday numerals are made up of the ten digits:

For example: The numeral \(867\) is made up of the 3 digits "8","6" and "7".

For example: The numeral \(29\) is made up of the 2 digits "2" and "9".

For example: The numeral \(3\) is made up of the single digit "3".

For example: The numeral \(867,389,272\) is made up of the 9 digits "8","6","7","3","8","9","2","7" and "2".

You can use digits to build numerals that are as long as you like! The numbers keep going on forever and ever, and so do the numerals that we use to write them.