# What is a “decade” as a unit of measure (ex. a decade of the EM spectrum)?

Reading through papers and online sources about radio galaxies, I kept stumbling across a term--a "decade" of the electromagnetic spectrum. Radio galaxy emission encompasses "11 decades of the EM spectrum". Or this quote from NASA:

Astronomers have made observations of electromagnetic radiation from cosmic sources that cover a range of more than 21 decades in wavelength (or, equivalently in frequency or energy)!

Source.

What exactly does this term correspond to?

Note: I used the tag because of the context, but I am not sure if the unit can be used outside of the field. Feel free to edit away!

From 10Hz to 100Hz is a decade (on a logarithmic axis this is $10^2$ to $10^3$).

• Thanks for the quick response! So a decade is 10^(x) to 10^(x+1) range? When they say "11 decades" they mean that radio galaxies emit light with wavelengths from (for example, not sure if this is accurate) 10^(-1) m to 10^(10)m? – Joseph Farah Mar 15 '18 at 20:43
• @JosephFarah yes. – DanielSank Mar 16 '18 at 2:06
• Outside of log-scaled stuff like wavelengths and frequencies, you're much more likely to encounter the phrase "order of magnitude" to describe a 10x difference. However, it would be wrong (or at least, imprecise) to use that phrase for a log-scaled unit because an increase of 10x is "not a big deal" in that context (compared to a linear context where a 10x increase is a huge deal). – Kevin Mar 16 '18 at 3:02
• Ok, it isn't a formal answer. However, from my point of view, sometimes a short examples is better than a long formal definition – MatMorPau22 Mar 16 '18 at 15:07
• Examples are fine. Not explaining what in blazes you're talking about isn't. I couldn't make any sense of the example without reading the other answers. – jpmc26 Mar 16 '18 at 20:57

While many units are available for physical measurables, there are only a few that identify unitless variables, like ratios.

One is 'octave', meaning a factor of two (usually in frequency); another is 'decade', meaning a factor of ten. A third is bel, which grows a suffix from time to time, and indicates (almost always) a factor of ten in power. The tenth-of-a-bel, decibel, is denoted 'dB'.

Percent, parts-per-million, pH, are also unitless.

Any attempt to line-fit data on log/log or semilog plots will involve one or more axes being unitless, and give rise to phrases like 'dB per octave'. When your data is spread over a 100:1 range, it might look best on two-decade semilog paper.

• Ahh...semilog paper. Great for feeding a chart recorder plugged to a transimpedance amplifier. Now just to find those punchcards so we can analyze the data. – J... Mar 16 '18 at 11:31
• The kind of naming convention that makes “octave” a factor of 2, but “decade” a factor of 10, makes me cry of pain. – Emil Jeřábek Mar 16 '18 at 15:38
• There are eight (diatonic) tones in a musical octave, not seven, @EmilJeřábek. Seven tones only gets you to the seventh scale degree, not to the octave. – Beanluc Mar 16 '18 at 16:50
• @Beanluc Count with me: C=0 D=1 E=2 F=3 G=4 A=5 B=6 C=7. These are seven steps, not eight. – Emil Jeřábek Mar 16 '18 at 17:15
• Seven steps, yes. Seven tones? Count again. The number of tones, not the number of steps, is why it's called an octave. – Beanluc Mar 16 '18 at 20:28

A decade is a factor of $10$, so it's a way of assigning a unit to the common logarithm ($\mathrm{log}_{10}$). It's also frequently assigned the unit symbol $\mathrm{dex}$.

## protected by Qmechanic♦Mar 16 '18 at 13:03

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).