What is a mantissa, and can you provide an example to explain it?

The term mantissa refers to the significant digits of a number in scientific notation. In a scientific notation format, a number is expressed as the product of a number (the mantissa) and a power of ten. For example, in the number 6.02 x 10^23, the mantissa is 6.02, while 10^23 is the exponential part that indicates the scale of the number.

To break this down further:

• Scientific Notation: This format is especially useful for representing very large or very small numbers in a more compact form. The general structure is m x 10^n, where m is the mantissa and n is the exponent.
• Example: Let’s take the number 0.000345. In scientific notation, this can be written as 3.45 x 10^-4. Here, 3.45 is the mantissa, while -4 is the exponent.

The concept of the mantissa is not just limited to scientific notation; it also appears in other areas of mathematics and computer science, such as logarithms and floating-point representation in programming. Understanding the mantissa helps in grasping how numbers are scaled and represented in different contexts.