Base 10 Number System

Our number system is a base ten system, and is based on groups (powers) of tens. It is a place value system, which means digits are placed in specific order to indicate the value that the digit brings to the number.

Other number systems may be based on additive, subtractive, or character patterns. The face value of a digit is what you see; the digit names itself. For example, the digit five in the number 453 has a face value of five. The digit four has a face value of four, and the digit three has a face value of three.

The place value of a digit is the value of the position that it occupies. In a base ten system, place values consist of powers of ten, starting with an exponent of zero. We label the base ten place values as units (100 = 1), tens (101), hundreds (102), thousands (103), etc.

Expanded form decomposes a number into its face and place values. For example,

5,602 = (5 x 1000) + (6 x 100) + (0 x 10) + (2 x 1)

Notice that each and every face value and its corresponding place value must be represented in the expanded form of the number. Expanded form can be extended when using decimal numbers by using any appropriate place value notation (fraction, exponent, or decimal form). For example,

450.85 = (4 x 100) + (5 x 10) + (0 x 1) + (8 x 1/10) + (5 x 1/100)