Writing Floating-Point Numbers

C++ has two ways of writing floating-point numbers. The first is to use the standard decimal-point notation you’ve been using much of your life:

12.34             // floating-point
939001.32         // floating-point
0.00023           // floating-point
8.0               // still floating-point

Even if the fractional part is 0, as in 8.0, the decimal point ensures that the number is represented in floating-point format and not as an integer. (The C++ Standard does allow for implementations to represent different locales—for example, providing a mechanism for using the European method of using a comma instead of a period for the decimal point. However, these choices govern how the numbers can appear in input and output, not in code.)

The second method for representing floating-point values is called E notation, and it looks like this: 3.45E6. This means that the value 3.45 is multiplied by 1,000,000; the E6 means 10 to the 6th power, which is 1 followed by 6 zeros. Thus 3.45E6 means 3,450,000. The 6 is called an exponent, and the 3.45 is termed the mantissa. Here are more examples:

2.52e+8             // can use E or e, + is optional
8.33E-4             // exponent can be negative
7E5                 // same as 7.0E+05
-18.32e13           // can have + or - sign in front
1.69e12             // 2010 Brazilian public debt in reais
5.98E24             // mass of earth in kilograms
9.11e-31            // mass of an electron in kilograms

As you might have noticed, E notation is most useful for very large and very small numbers.

E notation guarantees that a number is stored in floating-point format, even if no decimal point is used. Note that you can use either E or e, and the exponent can have a positive or negative sign (see Figure 3.3). However, you can’t have spaces in the number, so, for example, 7.2 E6 is invalid.

Figure 3.3. E notation.

To use a negative exponent means to divide by a power of 10 instead of to multiply by a power of 10. So 8.33E-4 means 8.33 / 10⁴, or 0.000833. Similarly, the electron mass 9.11e-31 kg means 0.000000000000000000000000000000911 kg. Take your choice. (Incidentally, note that 911 is the usual emergency telephone number in the United States and that telephone messages are carried by electrons. Coincidence or scientific conspiracy? You be the judge.) Note that –8.33E4 means –83300. A sign in front applies to the number value, and a sign in the exponent applies to the scaling.