What are floating-point numbers?
A floating-point number is a number that has a fractional part; it is written with a decimal point, e.g.: 2.5, 3.141, -5.99. Floating point numbers are distinguished from integers, which have no fractional part. In Java, there are two types of floating-point numbers, those of type float and those of type double. Numbers of type double have higher precision than those of type float. By default, we will use double for floating-point numbers in CS111.
There are several ways to represent real numbers on computers. Fixed point places a radix point somewhere in the middle of the digits, and is equivalent to using integers that represent portions of some unit. For example, one might represent 1/100ths of a unit; if you have four decimal digits, you could represent 10.82, or 00.01. Another approach is to use rationals, and represent every number as the ratio of two integers. Floating-point representation – the most common solution – basically represents reals in scientific notation. Scientific notation represents numbers as a base number and an exponent. For example, 123.456 could be represented as 1.23456 × 102. In hexadecimal, the number 123.abc might be represented as 1.23abc × 162. Floating-point solves a number of representation problems. Fixed-point has a fixed window of representation, which limits it from representing very large or very small numbers. Also, fixed-point is prone to a loss of precision when two large numbers are di
