Electronics For Dummies by Cathleen Shamieh

Author:Cathleen Shamieh
Language: eng
Format: mobi, epub, pdf
ISBN: 9781119117988
Published: 2015-08-03T20:30:47+00:00

Adding bits of numbers

In the decimal (base 10) system, if you want to express a number greater than 9, you need to use more than one digit. Each position, or place, in a decimal number represents a power of ten (100, 101, 102, 103, and so forth), and the value of the digit (0–9) sitting in that position is a multiplier for that power of ten. With powers of ten, the exponent (that tiny number raised up next to the 10) tells you how many times to multiply 10 times itself, so 101 equals 10, 102 equals 10 × 10 which is 100, 103 equals 10 × 10 × 10 which is 1,000, and so on. As for 100, it just equals 1 because any number raised to the zeroth power equals 1. So the positions in a decimal number, starting from the rightmost position, represent 1, 10, 100, 1,000, and so forth. These are also known as place values (ones or units, tens, hundreds, thousands, and so forth). The digit (0–9) sitting in that position (or place) tells you how many ones, tens, hundreds, thousands, and so forth are contained in that decimal number.

For example, the number 9,452 can be written in expanded notation as

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