Place+Value+and+Notations

The **decimal system** is a system of writing numbers based on the number ten. A number written in the decimal system is said to be in **decimal notation**. In decimal notation, the smallest ten **whole numbers** need only one digit. Today we write them as 0,1,2,3,4,5,6,7,8, and 9. Two digits are needed to write the next ninety whole numbers as decimals. 10 11 12 13 ... 19 20 21 ... 99 Notice that we call the whole numbers //decimals// even though there are no decimal points. The next nine hundred whole numbers can be written with three digits. 100 101 102 ... 200 201 ... 999 By using more digits, very large numbers can be written. The 1990 census estimate of the U.S. population was 248709873 people. To make this easier to read, groups of digits are separated by commas. **In Decimal Notation** //248,709,873// **In English** //Two hundred forty-eight million, seven hundred nine thousand, eight hundred seventy-three//. Usually decimal notation is shorter than English words. Each digit in a decimal has a **place value**.
 * WHAT IS THE DECIMAL SYSTEM?**


 * STANDARD NOTATION**-writing numbers using the digits (5,425,203)


 * EXPANDED NOTATION**-writing numbers using the individual place values (643 = 600+40+3) OR (6 x 100)+(4 x10)+(3x1)


 * NUMBER AND WORD NOTATION**-writing numbers in "short-hand" using words and numbers (65,000,000 = 65 million) OR (65,000,000 = 6.5 million)


 * EXPONENTIAL NOTATION**-writing large numbers with exponents (8⁴ = 8x8x8x8 = 4096)