Decade (log scale)

More generally, to write a number in the form a × 10b, where 1 <= a < 10 and b is an integer, is to express it in scientific notation, and a is called the significand or the mantissa, and b is its exponent.

[3] The numbers so expressible with an exponent equal to b span a single decade, from

Decades are especially useful when describing frequency response of electronic systems, such as audio amplifiers and filters.

Decades on a logarithmic scale, rather than unit steps (steps of 1) or other linear scale, are commonly used on the horizontal axis when representing the frequency response of electronic circuits in graphical form, such as in Bode plots, since depicting large frequency ranges on a linear scale is often not practical.

The example Bode plot shows a slope of −20 dB/decade in the stopband, which means that for every factor-of-ten increase in frequency (going from 10 rad/s to 100 rad/s in the figure), the gain decreases by 20 dB.

Four powers of 10 spanning a range of three decades: 1, 10, 100, 1000 (10 0 , 10 1 , 10 2 , 10 3 )
Four grids spanning three decades of resolution: One thousand 0.001s, one-hundred 0.01s, ten 0.1s, one 1.
Bode plot showing the concept of a decade: each major division on the horizontal axis is one decade