The blood pressure of 100mmHg noted in one printer thus lies beyond the 95% limit of 97 but within the 99.73% limit of 101.5 (=88+(3x4.5)). You can use them to express uncertainty about the past: Sheila cant have gone to the shops. This is because the variables in transient testing include voltage or current parameters, time domain parameters and set-up parameters, and there is no meaningful way to combine these into a budget expressing a single value which could then represent the . Week 4 weight: 5.4 lb. In more general terms, uncertainty can be thought of as a disclaimer for your measured values. The zeros in 0.053 are not significant, because they are only placekeepers that locate the decimal point. As noted above, if random samples are drawn from a population their means will vary from one to another. A method of evaluating and expressing uncertainty in measurement adapted from NIST Technical Note 1297. Brief summary: The probability of roughly 68% that is provided by the standard uncertainty is often too low for the users of measurement uncertainty. This indicates a low precision, high accuracy measuring system. These means generally conform to a Normal distribution, and they often do so even if the observations from which they were obtained do not. A high school track coach has just purchased a new stopwatch. Its also quite common to add other forms to these modals, especially going to, have to and used to., It was after eleven, so they cant have been going to meet Andy. One method of expressing uncertainty is as a percent of the measured value. Do you want me to check again?, It mustve rained! Chapter 5. In practice, we often want to compare two groups, commonly to determine whether or not they are different. The force \(F\) on an object is equal to its mass m multiplied by its acceleration \(a\). These measurements were relatively precise because they did not vary too much in value. Here's how you can help: One: Model Calmness and Clarity: "Keep Calm and Carry On" is more than a WWII slogan, it's still the best advice for leaders during crises. It should be noted that the last digit in a measured value has been estimated in some way by the person performing the measurement. . For every situation, there are numerous possible outcomes. An official website of the United States government. I reckon were only going to be a few minutes late.. Listen to these two clips . The Activity pages appear in the menu entitled 'This Unit' in the upper right. The simplest way is to express the distribution in terms of a probability density function (PDF). For example, the person measuring the length of a stick with a ruler notices that the stick length seems to be somewhere in between 36.6cm and 36.7cm, and he or she must estimate the value of the last digit. She mustve taken the dog out for a walk, Sales cant be going down! All measurements contain some amount of uncertainty. The scientific uncertainty surrounding climate change research can be difficult to communicate to policy makers and the public 5. Irregularities in the object being measured. For example, if you use a standard ruler to measure the length of a stick, you may measure it to be 36.7cm. If you are given proportions, you can either convert these to percentages (multiply by 100), or use the modified formula below: \({\rm{SE\;proportion}} = {\rm{\;}}\sqrt {\frac{{p\;\left( {1 - p} \right)}}{n}}\). "Error" in this context is the difference between a measured and true value. For example, a series of samples of the body temperature of healthy people would show very little variation from one to another, but the variation between samples of the systolic blood pressure would be considerable. Reporting Verbs in English: 27 Words for Say, How to Express Uncertainty in English (Everything You Need to Know), Ways of Looking in English: Ogle, Gaze, Gawk and 12 Others, Carols not here. Nothing's ready! You can, of course, use a mixture of these strategies. PDF Accuracy, Precision and Uncertainty - University of Utah General formulae for confidence intervals. (4) Ipart (2) you expressed uncertainty as standard deviation. Its basically a little less certain than almost definitely., When we use apparently, its like were saying, I dont know for sure, but someone told me this.. (Accessed March 4, 2023), Created July 28, 2020, Updated July 29, 2020, Manufacturing Extension Partnership (MEP). The distance of the new observation from the mean is 4.8-2.18=2.62. 95% CI for proportion of males 39.2 (1.96 x 4.46) = 30.5 and 47.9. You will note that an answer given to three digits is based on input good to at least three digits, for example. Thats when you need to express uncertainty in English. Let us consider an example of a GPS system that is attempting to locate the position of a restaurant in a city. . Uncertainty is a quantitative measure of how much your measured values deviate from a standard or expected value. Using the first option, we calculate 95% confidence intervals for the prevalence of teenage pregnancy in 2005 and 2015: 95% CI in 2005 = 49 (1.96 x 49) = (35.3, 62.7), 95% CI in 2015 = 25 (1.96 x 25) = (15.2, 34.8). - When you are still thinking about a situation. Legal. 2. Most of us have had the experience of being persuaded by someone simply because they were so sure about what they . For both these sentences, were 100% sure about these facts: What if you need to express something in the middle? Answer (1 of 4): Heisenberg's uncertainty principle gives mathematical expression to the statement that for subatomic particles it is impossible to know both the momentum and the position of the particle at the same time. We can conclude that the weight of the apple bag is \(5lb8%\). For example, a single value can be used to express the uncertainty and compare it between different measurement methods, even when its distribution is asymmetric and would otherwise . Can you think of a different way to express the uncertainty of your measurement? Activity 1 contains four example sentences. OK. Over to you. Specify the measurement process. As far as I know, the cat must be sleeping right now., I think we possibly mightve given the cat too much coffee., I believe the cat might start a world war. Question: (4) In part (2) you expressed uncertainty as standard deviation. Suppose you have a range for one measurement, such as a pipet's tolerance, and standard deviations for the other measurements. Solved Provide explanations of your decisions or | Chegg.com In our paper example, the length of the paper could be expressed as 11 in. 0.2. Explore size estimation in one, two, and three dimensions! Gabriel Clark is an English teacher with 18 years experience and an MA in TESOL and Applied Linguistics from Portsmouth University. The relative uncertainty gives the uncertainty as a percentage of the original value. Thus, the measured values deviated from each other by at most 0.3 in. 2. However, speakers of Spanish or French know it well, because they communicate theoretical ideas with "if," "might," or "maybe" by conjugating subjunctive verb forms. For example, a standard ruler can measure length to the nearest millimeter, while a caliper can measure length to the nearest 0.01 millimeter. A consequence of this is that, if two or more samples are drawn from a population, the larger they are the more likely they are to resemble each other - again provided that the random technique is followed. Anything outside the range is regarded as abnormal. In the previous three sections, we calculated the standard error of a single group. . (PDF) Uncertainty vs. Variability: What's the Difference and Why is it Uncertainty, Error, and Confidence | Process of Science | Visionlearning I don't think there can be any doubt about . The standard error is therefore 36 = 6. . By learning to be okay . There is precisely the same relationship between a reference range and a confidence interval as between the standard deviation and the standard error. For example, a GP in a busy practice sees 36 patients in a given day. If your measurements are not very accurate or precise, then the uncertainty of your values will be very high. With small samples - say fewer than 30 observations - larger multiples of the standard error are needed to set confidence limits. If you do not do this, you will have a decimal quantity, not a percent value. How big is the uncertainty in something you calculate by multiplication or division? This is quite a formal expression. The concentration and uncertainty for Cu 2 + is 7.820 mg/L 0.047 mg/L. One of the most important ways we can invest in ourselves is to comfort ourselves in healthy ways. How to calculate uncertainty. One element of the form is the expression of certainty and uncertainty. One of the children had a urinary lead concentration of just over 4.0 mol/24h. The expression levels were estimated using the 2 Ct method. It is important to realise that we do not have to take repeated samples in order to estimate the standard error; there is sufficient information within a single sample. The expression level in eggs was used as a standard to compare expression levels among developmental stages, and the expression . A grocery store sells 5-lb bags of apples. (Expressed as an area this is 0.36m2, which we round to \(0.4\,m^2\) since the area of the floor is given to a tenth of a square meter.). Examples include the number of cardiac arrests in an A&E department every year, or the number referral rate from primary care to a specialist service per 1,000 patients per year. Table 13.4.1 summarizes the different units of concentration and typical applications for each. However, if the measured values had been 10.9, 11.1, and 11.9, then the measurements would not be very precise because there would be significant variation from one measurement to another. Dont worry!, Its probable Its probable that were going to get a big bonus this year!, Im pretty sure Im pretty sure that youre not supposed to push that button!, I think I think we should do that again!, I dont think I dont think he knows what hes talking about., I reckon I reckon you need another cup of coffee., I believe I believe they told us theyd be here at eight., Its possible Its possible that they forgot to leave the WiFi password., Theres a chance Theres a chance that well miss the flight if we dont leave now., I imagine I imagine itd be easy to get into the party., I suppose I suppose theres a long queue for that one. What kind of changes do you think will happen in your country over the next ten years? When the molar mass of the solute and the density of the solution are known, it becomes relatively easy with practice to convert among the units of concentration we have discussed, as illustrated in Example 13.4.3. Comprehensive analysis of the role of ICOS ( CD278 ) in pan-cancer Additionally, the content has not been audited or verified by the Faculty of Public Health as part of an ongoing quality assurance process and as such certain material included maybe out of date. In the equation above, the numerical value 1.96 relates to the 95% confidence level. How To Calculate Uncertainty in 7 Steps (Plus Examples) They are discussed further in Standard Statistical Distributions (e.g. As this confidence interval does not include the value of no difference (i.e. The uncertainty of the measurement result y arises from the uncertainties u (x i) (or u i for brevity) of the input estimates x i that enter equation (2). Furthermore, it is a matter of common observation that a small sample is a much less certain guide to the population from which it was drawn than a large sample. The prevalence of teenage pregnancies in a city was 49 per 1000 in 2005 and 25 per 1000 in 2015. The expression of ICOS in different cancer cell lines. Precision of measured values refers to how close the agreement is between repeated measurements. This is the 99.73% confidence interval, and the chance of this interval excluding the population mean is 1 in 370 (i.e. To the best of my knowledge, no similar book has been published. This would give an empirical normal range. Then you drop off 6.052-kg of potatoes at your laboratory as measured by a scale with precision 0.001 kg. A Leader's Guide To Managing Employee Uncertainty - Forbes But because the radius has only two significant figures, it limits the calculated quantity to two significant figures or. In some topics, particularly in optics, more accurate numbers are needed and more than three significant figures will be used. MAKING CONNECTIONS: REAL-WORLD CONNECTIONS FEVERS OR CHILLS? and the highest value was 11.2 in. In our sample of 72 printers, the standard error of the mean was 0.53 mmHg. If you have any concerns regarding content you should seek to independently verify this. Confidence intervals provide the key to a useful device for arguing from a sample back to the population from which it came. In Activity 2, students are asked to compare examples and decide which ones express the most uncertainty and which the least. We can use the following equation to determine the percent uncertainty of the weight: \(\text{% unc} =\frac{0.4 lb}{5 lb}100%=8%\). Speaker 2: Yes, I am sure/certain that he will have a good grade. Zeros are significant except when they serve only as placekeepers. . LAX is about 59 minutes from Harvey Mudd by car. This option enables a valid combination of the two uncertainties to be made in the usual way, but in log space, producing a combined . A good example is a determination of work done by pulling a cart on an incline that requires measuring the force and the distance independently. The standard error of the mean of one sample is an estimate of the standard deviation that would be obtained from the means of a large number of samples drawn from that population. These measurements are quite accurate because they are very close to the correct value of 11.0 inches. Of course. Uncertainty principle | Definition & Equation | Britannica Just by adding a short phrase like "I think" or "I reckon" to the . I have no doubt about it. Solved (4) In part (2) you expressed uncertainty as standard | Chegg.com In practice, we often want to compare two groups, commonly to determine whether or not they are different. PDF Propagation of Uncertainty through Mathematical Operations ) or https:// means youve safely connected to the .gov website. This plots the relative likelihood of the various possible values, and is illustrated schematically below: . These are count data, and we will use the relevant standard error formula given above. Using the method of significant figures, the rule is that the last digit written down in a measurement is the first digit with some uncertainty. Look at the puddles!, That guy cant be getting nearer. If a series of samples are drawn and the mean of each calculated, 95% of the means would be expected to fall within the range of two standard errors above and two below the mean of these means. PDF Experimental Uncertainties (Errors) - Purdue University However, uncertainty is when nothing is ever decided or sure. Next, we identify the least precise measurement: 13.7 kg. Turn the oven off!, "They can't be starting in an hour! Given a sample of disease-free subjects, an alternative method of defining a normal range would be simply to define points that exclude 2.5% of subjects at the top end and 2.5% of subjects at the lower end. Certainty and uncertainty. That is, you are indicating that the actual mileage of your car might be as low as 44,500 miles or as high as 45,500 miles, or anywhere in between. As part of this process, we are required to calculate a pooled standard error of the two groups. One way of comparing two groups is to look at the difference (in means, proportions or counts) and constructing a 95% confidence interval for the difference (see below). Note that the above formula uses percentages. Now we will use the second approach calculating the difference between the two prevalence rates. which for the appendicitis data given above is as follows: \({\rm{SE\;percentage}} = {\rm{\;}}\sqrt {\frac{{60.8 \times 39.2}}{{120}}}\). There is much confusion over the interpretation of the probability attached to confidence intervals. We know that 95% of these intervals will include the population parameter. The momentum of a particle is equal to the product of its mass times its velocity. When adding or subtracting measured values, the final answer cannot contain more decimal places than the least precise value. Quoting your uncertainty in the units of the original measurement - for example, 1.2 0.1 g or 3.4 0.2 cm - gives the "absolute" uncertainty. Calculate the deviation of each measurement, which is the absolute value of the difference between each measurement and the average value: (1.6.2) d e v i a t i o n = | measurement average |. In this lesson, you'll learn to express doubt and uncertainty the RIGHT way. I'm positive. The series of means, like the series of observations in each sample, has a standard deviation. We can say that the probability of each of such observations occurring is 5%. If we take the mean plus or minus three times its standard error, the interval would be 86.41 to 89.59. Simple Guide for Evaluating and Expressing the Uncertainty of - NIST .20004 19997 00007 = For example, one might express the uncertainty as the half range of the set, so one would express the measurement above as wgrams= 2 0000 000035.. You can be very sure that something DID happen (on the left of the table). Thus, in the example of equation (3), the uncertainty of the estimated value of the power P arises from the uncertainties of the estimated values of the potential difference V, resistance R 0 . What if the uncertainty of the thermometer were 3.0C? This can be proven mathematically and is known as the "Central Limit Theorem". Scientific uncertainty is a quantitative measurement of variability in the data. There are several ways to do this. Table 2 Probabilities of multiples of standard deviation for a Normal distribution. For each sample calculate a 95% confidence interval. I might not have locked the front door. If a measurement A is expressed with uncertainty, \(A\), the percent uncertainty (%uncertainty) is defined to be, \[\% \,\text{unc} =\dfrac {A}{A} \times 100\%\], Example \(\PageIndex{1}\): Calculating Percent Uncertainty: A Bag of Apples. 1 C ). This formula is only approximate, and works best if n is large and p is between 0.1 and 0.9. Lab B - Percent Error and Percent Difference - WebAssign We first calculate the pooled standard error, followed by the 95% confidence interval, as follows: \({\rm{Pooled\;SE}} = {\rm{\;\;}}\sqrt {{\lambda _1} + \;{\lambda _2}\;} = \;\sqrt {49 + \;25\;} = 8.6\), \(95{\rm{\% \;CI\;for\;difference}} = ({\lambda _1} - \;{\lambda _2})\). You purchase four bags over the course of a month and weigh the apples each time. This probability is small, so the observation probably did not come from the same population as the 140 other children. Use that different way to calculate it. the difference between the maximum and minimum values of the set. First, observe that the expected value of the bags weight, \(A\), is 5 lb. When youre expressing uncertainty in English with modal verbs, you might want to ask yourself two questions: As you can see, you can be very sure something DIDNT happen (on the right of the table). When we feel uncertain or insecure, our brain tries to rescue us by activating our dopamine systems. Thus, the answer is rounded to the tenths place, giving us 15.2 kg. ", OK. The ANOVA showed a main effect of uncertainty communication format [ F(2, 1119) = 11.03, P < 0.001; 2 = 0.02 ]. Examples 3 and 4 show slightly more certainty than 1 and 2. Lets practice expressing uncertainty in English. Percent difference is used when comparing two experimental results E1 and E2 that were obtained using two different methods. So we know what level of certainty the modal verbs express. While there is no subjunctive mood or verb form in Japanese, there are several ways to express uncertainty. 1; the zeros in this number are placekeepers that indicate the decimal point, 6; here, the zeros indicate that a measurement was made to the 0.1 decimal point, so the zeros are significant, 5; the final zero indicates that a measurement was made to the 0.001 decimal point, so it is significant, 4; any zeros located in between significant figures in a number are also significant. Uncertainty for Other Mathematical Functions. A .gov website belongs to an official government organization in the United States. differentiate: [verb] to obtain the mathematical derivative (see 1derivative 3) of. Brief summary. Uncertainty is a critical piece of information, both in physics and in many other real-world applications. Accuracy cannot be discussed meaningfully . Any other factors that affect the outcome (highly dependent on the situation). Measurement uncertainty for transient tests has to take a completely different approach to that for the other tests discussed so far. 2Rob Johnston, Analytic Culture in the US Intelligence Community (Washington, DC: Center for the Study of Intelligence 2005) p . You determine that the weight of the 5-lb bag has an uncertainty of 0.4lb. Can you think of a different way to express the uncertainty of your measurement? Lecture 3: Fractional Uncertainties (Chapter 2) and Propagation of Errors (Chapter 3) 7 Uncertainty with Two Variables The Pendulum Example The pendulum experiment is a good example of a calculated quantity, the ac-celeration due to gravity g, depending upon two measured quantities, a length l and a time T. As you know T = 2 v u u t l g If a measurement A is expressed . Seven Ways to Cope with Uncertainty - Greater Good The uncertainty in a measurement, A, is often denoted as A (delta A), so the measurement result would be recorded as A A. There are multiple ways to calculate uncertainty, some of which work better with different values . Evaluating, Expressing, and Propagating Measurement Uncertainty - NIST How do we express certainty and uncertainty? In contrast, if you had obtained a measurement of 12 inches, your measurement would not be very accurate. { "1.00:_Prelude_to_Science_and_the_Realm_of_Physics_Physical_Quantities_and_Units" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.01:_Physics-_An_Introduction" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.02:_Physical_Quantities_and_Units" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.03:_Accuracy_Precision_and_Significant_Figures" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.04:_Approximation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "1.E:_The_Nature_of_Science_and_Physics_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_The_Nature_of_Science_and_Physics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Kinematics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Two-Dimensional_Kinematics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Dynamics-_Force_and_Newton\'s_Laws_of_Motion" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Further_Applications_of_Newton\'s_Laws-_Friction_Drag_and_Elasticity" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_Uniform_Circular_Motion_and_Gravitation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_Work_Energy_and_Energy_Resources" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Linear_Momentum_and_Collisions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Statics_and_Torque" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10:_Rotational_Motion_and_Angular_Momentum" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "11:_Fluid_Statics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "12:_Fluid_Dynamics_and_Its_Biological_and_Medical_Applications" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "13:_Temperature_Kinetic_Theory_and_the_Gas_Laws" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "14:_Heat_and_Heat_Transfer_Methods" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "15:_Thermodynamics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "16:_Oscillatory_Motion_and_Waves" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "17:_Physics_of_Hearing" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "18:_Electric_Charge_and_Electric_Field" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "19:_Electric_Potential_and_Electric_Field" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "20:_Electric_Current_Resistance_and_Ohm\'s_Law" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "21:_Circuits_Bioelectricity_and_DC_Instruments" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "22:_Magnetism" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "23:_Electromagnetic_Induction_AC_Circuits_and_Electrical_Technologies" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "24:_Electromagnetic_Waves" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "25:_Geometric_Optics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "26:_Vision_and_Optical_Instruments" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "27:_Wave_Optics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "28:_Special_Relativity" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "29:_Introduction_to_Quantum_Physics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "30:_Atomic_Physics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "31:_Radioactivity_and_Nuclear_Physics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "32:_Medical_Applications_of_Nuclear_Physics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "33:_Particle_Physics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "34:_Frontiers_of_Physics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, 1.3: Accuracy, Precision, and Significant Figures, [ "article:topic", "authorname:openstax", "accuracy", "method of adding percents", "percent uncertainty", "precision", "significant figures", "license:ccby", "showtoc:no", "program:openstax", "licenseversion:40", "source@https://openstax.org/details/books/college-physics" ], https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FCollege_Physics%2FBook%253A_College_Physics_1e_(OpenStax)%2F01%253A_The_Nature_of_Science_and_Physics%2F1.03%253A_Accuracy_Precision_and_Significant_Figures, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), Precision of Measuring Tools and Significant Figures, Creative Commons Attribution License (by 4.0), source@https://openstax.org/details/books/college-physics, status page at https://status.libretexts.org.