2
Number Notations,
Arithmetical Operations,
and Calculators
DECIMAL NOTATION
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.
SCIENTIFIC 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-