Dividing Error Calculation
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metres long, but I’ve only got a 4 metre tape measure. I’ve also got a 1 metre dividing uncertainties ruler as well, so what I do is extend the tape error propagation square root measure to measure 4 metres, and then I measure the last metre with the ruler. The measurements
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I get, with their errors, are: Sponsored Links Now I want to know the entire length of my room, so I need to add these two numbers http://www.rit.edu/~w-uphysi/uncertainties/Uncertaintiespart2.html together – 4 + 1 = 5 m. But what about the errors – how do I add these? Adding and subtracting numbers with errors When you add or subtract two numbers with errors, you just add the errors (you add the errors regardless of whether the numbers are being added or subtracted). So for our room http://www.math-mate.com/chapter34_4.shtml measurement case, we need to add the ‘0.01m’ and ‘0.005m’ errors together, to get ‘0.015 m’ as our final error. We just need to put this on the end of our added measurements: You can show how this works by considering the two extreme cases that could happen. Say the measurement with our tape measure was over by the maximum amount – when we measured 4 m it was actually 3.99 m. Let’s also say that the ruler measurement was over as well by the maximum amount – so when we measured 1.00 m it was really 0.995 m. If we add these two amounts together, we get: This number is exactly the same as the lower limit of our error estimate for our added measurements: You’d find it would also work if you considered the opposite case – if our measurements were less than the actual distances. Adding or subtracting an exact number The error doesn’t change when you do something like
Google. Het beschrijft hoe wij gegevens gebruiken en welke opties je hebt. Je moet dit vandaag nog doen. Navigatie overslaan NLUploadenInloggenZoeken https://www.youtube.com/watch?v=QVNCZxNLKNI Laden... Kies je taal. Sluiten Meer informatie View this message in https://www.lhup.edu/~dsimanek/scenario/errorman/propagat.htm English Je gebruikt YouTube in het Nederlands. Je kunt deze voorkeur hieronder wijzigen. Learn more You're viewing YouTube in Dutch. You can change this preference below. Sluiten Ja, nieuwe versie behouden Ongedaan maken Sluiten Deze video is niet beschikbaar. WeergavewachtrijWachtrijWeergavewachtrijWachtrij Alles verwijderenOntkoppelen Laden... Weergavewachtrij Wachtrij __count__/__total__ Calculating error propagation Uncertainty (Error Values) in a Division Problem JenTheChemLady AbonnerenGeabonneerdAfmelden6969 Laden... Laden... Bezig... Toevoegen aan Wil je hier later nog een keer naar kijken? Log in om deze video toe te voegen aan een afspeellijst. Inloggen Delen Meer Rapporteren Wil je een melding indienen over de video? Log in om ongepaste content te melden. Inloggen Transcript Statistieken 3.408 weergaven Vind dividing error calculation je dit een leuke video? Log in om je mening te geven. Inloggen Vind je dit geen leuke video? Log in om je mening te geven. Inloggen Laden... Laden... Transcript Het interactieve transcript kan niet worden geladen. Laden... Laden... Beoordelingen zijn beschikbaar wanneer de video is verhuurd. Deze functie is momenteel niet beschikbaar. Probeer het later opnieuw. Gepubliceerd op 3 okt. 2013 Categorie Onderwijs Licentie Standaard YouTube-licentie Reacties zijn uitgeschakeld voor deze video. Autoplay Wanneer autoplay is ingeschakeld, wordt een aanbevolen video automatisch als volgende afgespeeld. Volgende Calculating Uncertainties - Duur: 12:15. Colin Killmer 10.837 weergaven 12:15 11 2 1 Propagating Uncertainties Multiplication and Division - Duur: 8:44. Lisa Gallegos 4.711 weergaven 8:44 Mod-02 Lec-06 Expectation Values & The Uncertainty Principle - Duur: 1:00:03. nptelhrd 8.674 weergaven 1:00:03 Physics - Chapter 0: General Intro (9 of 20) Multiplying with Uncertainties in Measurements - Duur: 4:39. Michel van Biezen 4.643 weergaven 4:39 Propagation of Uncertainty, Parts 1 and 2 - Duur: 16:31. Robbie Berg 21.912 weergaven 16:31 Uncertainty & Measurements - Duur: 3:01. TruckeeAPChemistry 18.679 weergave
"change" in the value of that quantity. Results are is obtained by mathematical operations on the data, and small changes in any data quantity can affect the value of a result. We say that "errors in the data propagate through the calculations to produce error in the result." 3.2 MAXIMUM ERROR We first consider how data errors propagate through calculations to affect error limits (or maximum error) of results. It's easiest to first consider determinate errors, which have explicit sign. This leads to useful rules for error propagation. Then we'll modify and extend the rules to other error measures and also to indeterminate errors. The underlying mathematics is that of "finite differences," an algebra for dealing with numbers which have relatively small variations imposed upon them. The finite differences we are interested in are variations from "true values" caused by experimental errors. Consider a result, R, calculated from the sum of two data quantities A and B. For this discussion we'll use ΔA and ΔB to represent the errors in A and B respectively. The data quantities are written to show the errors explicitly: [3-1] A + ΔA and B + ΔB We allow the possibility that ΔA and ΔB may be either positive or negative, the signs being "in" the symbols "ΔA" and "ΔB." The result of adding A and B is expressed by the equation: R = A + B. When errors are explicitly included, it is written: (A + ΔA) + (B + ΔB) = (A + B) + (Δa + δb) So the result, with its error ΔR explicitly shown in the form R + ΔR, is: R + ΔR = (A + B) + (Δa + Δb) [3-2] The error in R is: ΔR = ΔA + ΔB. We conclude that the error in the sum of two quantities is the sum of the errors in those quantities. You can easily work out the case where the result is calculated from the difference of two quantities. In that case the error in the result is the difference in the errors. Summarizing: Sum and difference rule. When two quantities are added (or subtracted), their determinate errors add (or subtract). Now consider multiplication: R = AB. With errors explicitly included: R + ΔR = (A + ΔA)(B + ΔB) = AB + (ΔA)B + A(ΔB) + (ΔA)(ΔB) [3-3] or : ΔR = (ΔA)B + A(ΔB) + (ΔA)(ΔB) This doesn't look like a simple rule. However, when we express the errors in relative form, things look better. When the error a is small relative to A and ΔB is small relative to B, then (ΔA)(ΔB) is certainly small relative to AB. It is also small compared to (ΔA)B a