Number Notations, Arithmetical Operations, and Calculators

One common representation of numbers is decimal notation. Typical examples are such large numbers as 807,267,434.51 and 3,500,000, and such small numbers as 0.00055 and 0.0000000000000000248. Decimal notation is often awkward to use, and it is embarrassingly easy to make foolish mistakes when carrying out arithmetical operations in this form. Most hand calculators will not accept extremely large or extremely small numbers through the keyboard in decimal notation. 

Another common, but more sophisticated, representation of numbers is scientific notation. This notation minimizes the tendency to make errors in arithmetical operations it is used extensively in chemistry. It is imperative that you be completely comfortable in using it. Hand calculators will accept extremely large or extremely small numbers through the keyboard in scientific notation. Ready and proper use of this notation requires a good understanding of the following paragraphs. 

An exponent is a number that shows how many times a given number (called the base) appears as a factor exponents are written as superscripts. For exam- 

Notice that we shifted the decimal point three places to the left, and we also increased the exponent on the 10 by the same number, three. In changing the form of a number but not its value, we always follow this basic rule. 

Decrease the lefthand factor by moving the decimal point to the left the same number of places as you increase the exponent of 10. An example is 2000 (i.e., 2000 x 10°) converted to 2 x 103. 

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