Frequency error in scientific notation - Page 1
Forum section: electronics / beginners

author: tkamiya
author_rank: Super Contributor
timestamp: February 02, 2019, 04:09:18 pm
content: I feel very dumb asking this but I'm confused.I've been tuning a Rb time base.Say output is 10MHz, and reading is 10.000,000,000,5Mhz, what is the error rate in scientific notation?Is it 5x10^11 or 5x10^12?For this, please ignore factors such as gate time and accuracy vs precision argument. I just want to know mathematically which is right.

author: awallin
author_rank: Frequent Contributor
timestamp: February 02, 2019, 04:26:59 pm
content: I get 5e-11 or 5*10^(-11)

author: Domagoj T
author_rank: Frequent Contributor
timestamp: February 02, 2019, 04:36:48 pm
content: Quote from: tkamiya on February 02, 2019, 04:09:18 pmThis is meaningless, unless you want to say it's a 10 GHz frequency, but thousand separator is not used on the right side of the decimal mark.What does the "." stand for and what does the "," stand for?Pick either one for thousand separator and don't use it for decimal.

author: tkamiya
author_rank: Super Contributor
timestamp: February 02, 2019, 04:54:08 pm
content: THAT depends on country you learned math. In United States, this is one of the valid expressions. Please note, the unit is MHz. So it's "slightly off" 10MHz. Therefore, decimal "." is in the right place. Thousand separator can go right and left.How do I know this? I work as a programmer for a major company. Numerical notation is a complex business. In some country, it even use "'" (apostrophe). There are at least 20 different way to write the same number.Either way, I would have hoped my intention was apparent from context.

author: tkamiya
author_rank: Super Contributor
timestamp: February 02, 2019, 05:02:04 pm
content: This makes me very happy. I am working with newly acquired Rb oscillator. Maximum drift seems to be 5 count in last digit, which is exactly the specification. At this kind of precision, it is challenging my GPSDO lab standard.

author: KE5FX
author_rank: Super Contributor
timestamp: February 02, 2019, 06:50:16 pm
content: I write software that's used all over the world, and I steadfastly refuse to use commas as decimal points, because that's both historically nonstandard and intensely stupid.One thing I like to do is write long numbers with spaces instead of periods or commas. 10.000 000 001 MHz is easy enough to interpret as an error of +1E-10. 10.000000001 MHz is hard to read at a glance and consequently more error-prone than necessary. 10.000,000,001 MHz is just a visual mess. 10,000.000.001 MHz is a catastrophe looking for a place to happen.

author: tkamiya
author_rank: Super Contributor
timestamp: February 02, 2019, 06:51:02 pm
content: Well, stupid for us Americans but business as usual for Europeans. The product I work on is used all over the world. As such, it needs to meet local conventions and often local laws. I don't have a freedom to force what I like. We have a huge routine just to do these number convention conversions.I thought math was international. I guess not quite so!

author: KE5FX
author_rank: Super Contributor
timestamp: February 02, 2019, 06:56:56 pm
content: Quote from: tkamiya on February 02, 2019, 06:51:02 pmNope. Usually it's us US-ians who change things for no good reason, but in this case it's the Europeans. I actually looked into this at one point, when I was curious to learn who thought it was a good idea to use the comma as a decimal point. It's a relatively modern change. What Iwasn'table to discover was the reason behind the change.This isn't a question of some old farts from the 1960s who refuse to switch from cycles per second to Hertz. It's literally the sort of thing that shows up in case studies after a bunch of people get killed. Unnecessary changes like this need to be fought, and fought hard.

author: tomato
author_rank: Regular Contributor
timestamp: February 02, 2019, 07:15:06 pm
content: Quote from: KE5FX on February 02, 2019, 06:56:56 pmCommas, decimals, and spacers are all acceptable, but the U.S. is in the minority using the decimal.(Re: 22nd CGPM, section 10)https://www.bipm.org/jsp/en/ListCGPMResolution.jsp?CGPM=22

author: tooki
author_rank: Super Contributor
timestamp: February 02, 2019, 07:23:18 pm
content: Quote from: KE5FX on February 02, 2019, 06:56:56 pmI couldn’t disagree more! In so many things, it’s the US that retains the historical form. In language, in units of measure, in styles of appliances, in construction... Europe and Asia are far more willing to change things — perhaps because Europe had a ton of reconstruction to do post WW2, and Asia was only just experiencing its economic boom at the time.

author: tooki
author_rank: Super Contributor
timestamp: February 02, 2019, 07:26:10 pm
content: Quote from: tomato on February 02, 2019, 07:15:06 pmHuh? That text in no way suggests that the point as the decimal is the minority. (The decimal is theseparator, whether it’s a comma or point.)

author: Benta
author_rank: Super Contributor
timestamp: February 02, 2019, 07:43:55 pm
content: Quote from: KE5FX on February 02, 2019, 06:56:56 pmI'm not certain what you mean by this. The decimal comma has been used at least since the 19th century in continental Europe, but Britain favoured the point.You reference to "modern change" must refer to computer technology, where the comma at some point was used to delimit lists, options and variables and as such could cause problems with numbers.That being said, I have two preferred options for presenting large numbers:10.000 000 000 5 (US/UK) or 10,000 000 000 5 (EU). This one is not my 1st favourite, as it can present problems in formating.10.000'000'000'5 (US/UK) or 10,000'000'000'5 (EU). I like it,as it's practically impossible to misinterpret and easy to read.In both cases, adding two zeros at the end would add to aesthetics.But everyone has his/her own style, I find clarity most important, speaking as an engineer.

author: IanB
author_rank: Super Contributor
timestamp: February 02, 2019, 07:51:13 pm
content: Quote from: tkamiya on February 02, 2019, 04:09:18 pmYour specified frequency is 10 MHz, and your reading is 10.000 000 000 5 MHz.Therefore the absolute error is (10.000 000 000 5 - 10) MHz = +0.000 000 000 5 MHzIn scientific notation this is +5 x 10-10MHz (you have to move the decimal 10 places to the left of the 5 to recover the original value).The relative error is (+5 x 10-10) MHz / 10 MHz = +5 x 10-11(no units).

author: IanB
author_rank: Super Contributor
timestamp: February 02, 2019, 07:55:52 pm
content: Quote from: Benta on February 02, 2019, 07:43:55 pmI believe there is an ISO standard for writing values in scientific and technical communications. Among other things I believe it prefers the use of "." as a decimal separator, that groups of three digits should be separated by a space, and that there should be a space between the value and the unit of measure (e.g. write 5 V not 5V).

author: Benta
author_rank: Super Contributor
timestamp: February 02, 2019, 08:01:30 pm
content: Quote from: tooki on February 02, 2019, 07:26:10 pmActually, that link is quite good, as it defines a rule that can be understood by anyone:Texts in English use decimal point.Texts in French, German, Russian (and other continental European languages) use decimal comma.What happens in other languages is apparently undefined.

author: tooki
author_rank: Super Contributor
timestamp: February 02, 2019, 08:09:52 pm
content: Quote from: Benta on February 02, 2019, 08:01:30 pmI wasn’t criticizing the quality of the text! (I agree with you that it’s quite clear.) I was only saying that it did not support tomato’s claim.

author: Domagoj T
author_rank: Frequent Contributor
timestamp: February 02, 2019, 08:38:43 pm
content: I always found comma as decimal separator as superior to point since it is more visible. I also find it easier to write than a point when writing fast by hand, or should I say, when writing fast a point often becomes a bit elongated and similar to comma. This can lead to confusion.As for thousand separator, for me a space is the only acceptable solution. Furthermore I don't think I've ever seen anything other than space on the right side of the decimal separator, but very often number is entirely concatenated.ISO 31-0 was used for this, but was superseded by ISO 80000-1. Unfortunately it is behind a paywall, but this references the standard and is available:http://www.ease.org.uk/wp-content/uploads/1-4.pdf

author: tomato
author_rank: Regular Contributor
timestamp: February 05, 2019, 03:57:25 am
content: Quote from: tooki on February 02, 2019, 07:26:10 pmI did not cite the CGPM as evidence that the U.S. is in the minority; only that commas, dots, and spaces are all accepted conventions.

author: ahbushnell
author_rank: Frequent Contributor
timestamp: February 05, 2019, 04:28:33 am
content: This is interesting.https://en.wikipedia.org/wiki/Decimal_separator

author: ahbushnell
author_rank: Frequent Contributor
timestamp: February 05, 2019, 04:30:43 am
content: Quote from: ahbushnell on February 05, 2019, 04:28:33 amhttps://en.wikipedia.org/wiki/ISO_80000-2

author: not1xor1
author_rank: Frequent Contributor
timestamp: February 05, 2019, 07:55:29 am
content: Quote from: KE5FX on February 02, 2019, 06:50:16 pm"Commas" is neither "historically non standard" nor "intensely stupid".ISO-8601 also stipulates normative notation based on SI conventions, adding that the comma is preferred over the full stop.Beisdes that you are a bad programmer. Usually most OSs provide APIs to interface to the different national standards.Hard coding decimal and thousands separators is really dumb and/or just another symptom of that sick "America first" attitude.