# Metric notation

#### Gulliveig

Joined May 29, 2013
2
Vol. 1 Ch. 4 "Metric notation"

"Because the major prefixes in the metric system refer to powers of 10 that are multiples of 3 (from "kilo" on up, and from "milli" on down), metric notation differs from regular scientific notation in that the significant digits can be anywhere between 1 and 1000, [...]"

The highlighted number should read 999, as 1000 would be represented by 1 with the next higher metrix prefix, e.g. 1000 kA -> 1 MA.

Regards,
Herb Glarner

#### Georacer

Joined Nov 25, 2009
5,182
Yes, you are correct. Even though in real life we don't impose the 1-999 rule. We choose the prefix of the unit first and then adjust the mantissa, which may throw it out of limits.

It's a valid correction though and will be documented.
Thanks!

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#### tshuck

Joined Oct 18, 2012
3,534
I would argue that it is correct, well, at least partially.
It says between 1 and 1000.

Less than 1, and you would use the next smaller prefix. Saying that a number between the two is exclusive of the two bounds. The point could be made, I'd tend to agree, that the 1 should be included, but limiting the wording to say between 1 and 999 would mean that both 1 and 999, are to use another prefix.

#### Georacer

Joined Nov 25, 2009
5,182
In any case, the wording needs work.

"Between 1 and 1000" and "from 1 to 1000" aren't easily distinguishable in human language.

Unless it wrote $$c \in [1,1000)$$, then it's not clear enough.

#### studiot

Joined Nov 9, 2007
4,998
Well pretty well every capacitor manufacturer makes 1000μF caps (and above). and labels them as such.

#### WBahn

Joined Mar 31, 2012
26,398
I'd also point out that the phrase "the significant digits can be anywhere between 1 and 1000" is confusing and wrong. The term "significant digits" refers to the digits that are significant. 42 is not a digit. Note that "digits" is, in general, plural. Each significant digit is between 0 and 9, inclusive. For example, given 42.03mA, all four digits are signficiant, but all four are between 0 and 9.

The fix is easy, just say that the prefix is nominally chosen such that the mantissa falls in the range

1.0 <= mantissa < 1000.0

But note that this is not a hard requirement and values such as 4700uF and 0.1uF are quite commonly used. Also, in some instances is more clear to use a consistent prefix in order to make value comparisons more obvious. So it might be better to compare 800V and 7000V instead of comparing 800V and 7kV.

#### studiot

Joined Nov 9, 2007
4,998
Also, in some instances is more clear to use a consistent prefix in order to make value comparisons more obvious. So it might be better to compare 800V and 7000V instead of comparing 800V and 7kV.
A very good example of Engineering Common Sense.

#### Dcrunkilton

Joined Jul 31, 2004
422
"Because the major prefixes in the metric system refer to powers of 10 that are multiples of 3 (from "kilo" on up, and from "milli" on down), metric notation differs from regular scientific notation in that the significant digits can be anywhere between 1 and 1000, [...]"

"Because the major prefixes in the metric system refer to powers of 10 that are multiples of 3 (from "kilo" on up, and from "milli" on down), metric notation differs from regular scientific notation in that the mantissa can be anywhere between 1 and 999, [...]"

credited to Gulliveig at ibiblio.org

Thanks to all for your assistance,

Dennis

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#### WBahn

Joined Mar 31, 2012
26,398
As a bit of a nit, the proper term is "significand" and not "mantissa". The word mantissa has a precise meaning as being the fractional part of a logarithm and the word "significand" is the preferred term. Notice that I used "mantissa" in my post above. That's because I wasn't aware of this at the time. So my recommendation would be to have a sentence at the proper place that points out the distinction and the proper term and then uses the proper term from that point on.