Numbers with fraction are called real numbers like
3.14159265... (π)
2.71828... (e: the Euler’s number)
0.000000001 or 1.0×10-9 (seconds in a nanosecond)
86,400,000,000,000 or 8.64×1013 (nanoseconds in a day)
The alternative notation for the last two numbers is called scientific notation, which has a single digit to the left of the decimal point.
Its format is
±d.ffff...×10±eeee...
Floating point describes a system for numerical representation in which a string of digits (or bits) represents a rational number.
For example, a fixed-point representation that has seven decimal digits, with the decimal point assumed to be positioned after the fifth digit, can represent the numbers
12345.67, 8765.43, 123.00, ...
whereas a floating-point representation with seven decimal digits could in addition represent
1.234567, 123456.7, 0.00001234567, 1234567000000000, ...
A number in scientific notation that has no leading 0s is called a normalized number and floating-point numbers should be normalized.
Examples of normalized FP numbers include
5.341×103 and -1.101101×2-3
and examples of not normalized FP numbers include
0.05341×105 and -1101.101×2-6
Normalized floating points have many advantages and hardware using them is standardized, therefore simplified.