In order to be confident in our use of numbers, we must understand how our number system works and how numbers are related to each other. We use a single number structure. All numbers in our single number structure can be represented using combinations of a finite set of digits--0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
An important understanding of how our number system works comes from understanding "place value." This means that a digit can carry a different value depending on where in a number it is located. We use a base 10 system. Depending on where a digit is placed, that digit represents a power of 10.
When learning about number systems, it is important to remember 3 things.
1.) Use of numbers in the world around us can take on many different forms.
2.) The same digit takes on different values depending on where it is placed .
3.) The number system is finite.
Below is an interactive chart that helps explain the different ideas behind the number system.
Ideally, what our numeral system does is it
- Represents a useful set of numbers
- Give every number represented a unique representation
- Reflect the algebraic and arithmetic structure of the numbers.