10.3. Exponential Notation

For both large and small numbers, an exponential notation can be useful. For example:

numeric digits 5
say 54321*54321

would display 2950800000 in the long form. Because this is misleading, the result is expressed as 2.9508E+9 instead.

The definition of numbers is, therefore, extended as follows:


>>-+------------+--+----------------------+--+-digits--------+---------->
   +-whitespace-+  +-sign--+------------+-+  +-digits.digits-+
                           +-whitespace-+    +-.digits-------+
                                             +-digits.-------+

>--+---------------------+--+------------+-------------------------><
   +-E--+------+--digits-+  +-whitespace-+
        +-sign-+

The integer following the E represents a power of ten that is to be applied to the number. The E can be in uppercase or lowercase.

Certain character strings are numbers even though they do not appear to be numeric, such as 0E123 (0 times 10 raised to the power of 123) and 1E342 (1 times 10 raised to the power of 342). Also, a comparison such as 0E123=0E567 gives a true result of 1 (0 is equal to 0). To prevent problems when comparing nonnumeric strings, use the strict comparison operators.

Here are some examples:

Example 10.5. Exponential notation

12E7   =    120000000           /* Displays "1" */
12E-5  =    0.00012             /* Displays "1" */
-12e4  =    -120000             /* Displays "1" */
0e123  =    0e456               /* Displays "1" */
0e123  ==   0e456               /* Displays "0" */

The results of calculations are returned in either conventional or exponential form, depending on the setting of NUMERIC DIGITS. If the number of places needed before the decimal point exceeds DIGITS, or the number of places after the point exceeds twice DIGITS, the exponential form is used. The exponential form the language processor generates always has a sign following the E to improve readability. If the exponent is 0, the exponential part is omitted--that is, an exponential part of E+0 is not generated.

You can explicitly convert numbers to exponential form, or force them to be displayed in the long form, by using the FORMAT built-in function (see Section 7.4.33, “FORMAT”).

Scientific notation is a form of exponential notation that adjusts the power of ten so that the number contains only one nonzero digit before the decimal point. Engineering notation is a form of exponential notation in which up to three digits appear before the decimal point, and the power of ten is always a multiple of three. The integer part can, therefore, range from 1 through 999. You can control whether scientific or engineering notation is used with the following instruction:


                 +-SCIENTIFIC------------+
>>-NUMERIC FORM--+-----------------------+--;------------------><
                 +-ENGINEERING-----------+
                 +-+-------+--expression-+
                   +-VALUE-+

Scientific notation is the default.

Example 10.6. Scientific notation

/* after the instruction */
Numeric form scientific

123.45 * 1e11     ->     1.2345E+13

/* after the instruction */
Numeric form engineering

123.45  * 1e11    ->    12.345E+12