Decimal number system

1. A system which permits numbers to be expressed according to the following rules:
   • Numbers consist of two parts, 𝑥 and 𝑦 in the form 𝑥.𝑦, where 𝑥 is an integer such that |𝑥| ≥ 1 and 𝑦 is a number such that 0 ≤ |𝑦| < 1.
   • Each digit in both 𝑥 and 𝑦 has a value between 0 & 9 inclusive.
   • The symbol separating 𝑥 from 𝑦 is called the decimal point.
   • Each digit represents a multiple of 10ⁿ, where n is a digit’s position relative to the decimal point. Because of this, numbers expressed in the decimal number system are said to be in base 10.
2. A radix of 10 can be appended to any number to remove any doubt it is a decimal number, for example: 501246.231₁₀.
3. In the table below each digit of the decimal number 501246.231 is converted into the value it represents.
   • 5 x 10⁵ + 0 x 10⁴ + 1 x 10³ + 2 x 10² + 4 x 10¹ + 6 x 10⁰ + 2 x 10^-1 + 3 x 10^-2 + 1 x 10^-3 = 501246.231.

4. Position	5	4	3	2	1	0	.	-1	-2	-3
   Value of ‘1’	105	104	103	102	101	100	.	10-1	10-2	10-3
   Example decimal number	5	0	1	2	4	6	.	2	3	1
   Value of digit	5 x 105	0 x 104	1 x 103	2 x 102	4 x 101	6 x 100	.	2 x 10-1	3 x 10-2	1 x 10-3