In mathematics, the mantissa refers to the fractional part of a logarithm or a floating-point number. It represents the digits after the decimal point in a logarithm or the significant digits in a normalized scientific notation representation of a number.

The term “mantissa” is commonly associated with logarithms, particularly in older mathematical literature. In a logarithm of the form log_b(x), the mantissa refers to the part that follows the decimal point. It provides information about the digits that contribute to the value of the logarithm.

For example, consider log_10(345.678). Here, the mantissa is 0.5378, which represents the fractional part of the logarithm.

Similarly, in floating-point representation, the mantissa represents the significant digits of a number in scientific notation. In this case, the mantissa is typically normalized, meaning it is adjusted to have a single non-zero digit to the left of the decimal point. The mantissa, along with the exponent and the base, forms the components of a floating-point representation.

For example, in the number 2.56 x 10^4, the mantissa is 2.56, which contains the significant digits of the number.

It’s important to note that with the increasing use of computers and standardized floating-point representations (such as the IEEE 754 standard), the term “mantissa” has been largely replaced by terms like “significand” or “fraction” to describe the fractional part of a floating-point number.

In summary, the mantissa refers to the fractional part of a logarithm or the significant digits in a floating-point number. It plays a role in representing and manipulating numbers in logarithmic or scientific notation formats.