In mathematics, the characteristic refers to the integer part of a logarithm or a floating-point number in scientific notation. It represents the integral component or the power of the base in logarithmic calculations or the exponent in scientific notation.

The characteristic is commonly associated with logarithms, particularly in older mathematical literature. In a logarithm of the form log_b(x), the characteristic represents the integer part of the logarithm. It provides information about the scale or magnitude of the number being represented.

For example, consider log_10(345.678). Here, the characteristic is 2, which represents the power of 10 that is required to obtain the value 345.678.

Similarly, in scientific notation, the characteristic refers to the exponent of the power of 10. In this case, the characteristic, along with the mantissa or significand, forms the components of a floating-point representation.

For example, in the number 2.56 x 10^4, the characteristic is 4, which indicates that the decimal point should be moved four places to the right to obtain the actual value.

It’s important to note that in scientific notation, the characteristic can be positive or negative, depending on whether the number is larger or smaller than 1, respectively. A positive characteristic indicates a value greater than 1, while a negative characteristic indicates a value less than 1.

In summary, the characteristic represents the integer part or exponent of a logarithm or a floating-point number in scientific notation. It provides information about the scale, magnitude, or position of the represented value in logarithmic or exponential form.