Arithmetic | Theory of computation | Computer arithmetic
Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $23.4476 with $23.45, the fraction 312/937 with 1/3, or the expression √2 with 1.414. Rounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid misleadingly precise reporting of a computed number, measurement, or estimate; for example, a quantity that was computed as 123,456 but is known to be accurate only to within a few hundred units is usually better stated as "about 123,500". On the other hand, rounding of exact numbers will introduce some round-off error in the reported result. Rounding is almost unavoidable when reporting many computations – especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating-point representation with a fixed number of significant digits. In a sequence of calculations, these rounding errors generally accumulate, and in certain ill-conditioned cases they may make the result meaningless. Accurate rounding of transcendental mathematical functions is difficult because the number of extra digits that need to be calculated to resolve whether to round up or down cannot be known in advance. This problem is known as "". Rounding has many similarities to the quantization that occurs when physical quantities must be encoded by numbers or digital signals. A wavy equals sign (≈: approximately equal to) is sometimes used to indicate rounding of exact numbers, e.g., 9.98 ≈ 10. This sign was introduced by Alfred George Greenhill in 1892. Ideal characteristics of rounding methods include: 1. * Rounding should be done by a function. This way, when the same input is rounded in different instances, the output is unchanged. 2. * Calculations done with rounding should be close to those done without rounding. 3. * As a result of (1) and (2), the output from rounding should be close to its input, often as close as possible by some metric. 4. * To be considered rounding, the range will be a subset of the domain, in general discrete. A classical range is the integers, Z. 5. * Rounding should preserve symmetries that already exist between the domain and range. With finite precision (or a discrete domain), this translates to removing bias. 6. * A rounding method should have utility in computer science or human arithmetic where finite precision is used, and speed is a consideration. Because it is not usually possible for a method to satisfy all ideal characteristics, many different rounding methods exist. As a general rule, rounding is idempotent; i.e., once a number has been rounded, rounding it again will not change its value. Rounding functions are also monotonic; i.e., rounding a larger number gives a larger or equal result than rounding a smaller number. In the general case of a discrete range, they are piecewise constant functions. (Wikipedia).
Basic Math - Using rounding to estimate sums
Rounding is an important process, but is really shines when we are estimating sum. This is because it is often easier to do rounded numbers in our head. Check out this video for some tips on this process. For more videos please visit http://www.mysecretmathtutor.com
From playlist Basic Math
Rounding Numbers and Rounding Decimals - The Easy Way!
This math video tutorial provides a basic introduction into rounding. It explains the process of rounding numbers and rounding decimals. Here is a list of topics: 1. Rounding numbers to the nearest ten 2. Rounding numbers to the nearest hundred 3. Rounding decimals to the nearest whol
From playlist GED Math Playlist
Rounding Decimals to a Desired Accuracy
Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Rounding Decimals to a Desired Accuracy. Here we look at a couple of examples of rounding decimals to a specified accuracy (tenths, hundredths, thousandths, e
From playlist All Videos - Part 2
This video provides an example of rounding a given decimal to different place values. Complete video list: http://www.mathispower4u.com
From playlist Introduction to Decimals
Algebra 1 11.2f - Rounding Repeating Decimals
Rounding repeating decimal numbers. From the Algebra 1 course.
From playlist Algebra 1 Chapter 11 (Selected videos)
Decimal Notation: Rounding Decimals
This video explains how to round decimals to a given place value. http://mathispower4u.com
From playlist Number Sense - Decimals, Percents, and Ratios
From playlist a. Numbers and Measurement
Coding Math: Mini #8 - Rounding
In this mini, we create a couple of VERY useful rounding functions that go above and beyond the built-in rounding functions you find in most languages. Support Coding Math: http://patreon.com/codingmath Source Code: http://github.com/bit101/codingmath
From playlist Minis
Rounding - tenths, hundredths, thousandths
rounding tenths (questions and answers) - https://bit.ly/3tYW0St rounding hundredths - https://bit.ly/2RtDHYk rounding thousandths - https://bit.ly/2T5HQSV
From playlist Number
Adrian Sieber - Round Round Song [Official Video HD]
Music video by Adrian Sieber performing his «Round Round Song». Get it on iTunes now: http://bit.ly/10h1NP2 http://www.adriansiebermusic.com/ https://www.facebook.com/adrian.sieber Directed by Danila for Kino Pravda & Toma 78 http://www.kinopravda.tv/ © 2013 Gadget Records Lyrics: I
From playlist Related Videos: The GIF's Visual Language In Music Videos
Power Query Defaults To Bankers Rounding Featuring Celia Alves - 2392
A very detailed discussion today about how Excel rounds. We were all taught in school that 8.4 rounds to 8 and 8.5 rounds to 9. But not in Power Query. Without letting you know, Power Query defaults to a rounding mode known as ASTM-E29 rounding or Banker's Rounding. In this scenario, anyth
From playlist Power Query
Excel Magic Trick 1333: Power Query (Get & Transform) Rounding: Banker's or Gaussian Rounding
Download Files: Start File: https://people.highline.edu/mgirvin/YouTubeExcelIsFun/EMT1333Start.xlsx Finish File: https://people.highline.edu/mgirvin/YouTubeExcelIsFun/EMT1333Finished.xlsx Download File: http://people.highline.edu/mgirvin/excelisfun.htm Learn about Banker’s Rounding or
From playlist Banker's Rounding or Half Way Even Rounding (Excel, Power Query, VBA)
rounding decimals (KristaKingMath)
► My Pre-Algebra course: https://www.kristakingmath.com/prealgebra-course In this video we learn how to round decimal numbers. Rounding is the process of simplifying several digits into one digit. For example, you might say that 794 is approximately 800, and in that case you're rounding t
From playlist Pre-Algebra
Excel Magic Trick 521: Bankers Rounding (Half-Way-Even) vs. Arithmetic Rounding
Download Files: https://people.highline.edu/mgirvin/YouTubeExcelIsFun/EMT516-523.xls See how to Round numbers two different ways: 1.School Rounding: 5 or greater add 1, 4 or less leave as is. 2.Bankers Rounding : 5 round to nearest even, 6 or greater add 1, 4 or less leave as is. See f
From playlist Banker's Rounding or Half Way Even Rounding (Excel, Power Query, VBA)
Excel Magic Trick #237: ROUND to Digit or Multiple
Download Excel Start File: h https://people.highline.edu/mgirvin/YouTubeExcelIsFun/EMT233-245.xls Download Excel Finished File: https://people.highline.edu/mgirvin/YouTubeExcelIsFun/EMT233-245Finished.xls Full Page With All File Links: https://people.highline.edu/mgirvin/YouTubeExcelIsFun/
From playlist Excel Series: Magic Tricks (2nd 200 videos)
Dead Or Alive - You Spin Me Round (Like a Record) (Official Video)
Official 4K Video for "You Spin Me Round (Like a Record)" by Dead Or Alive Listen on Spotify - http://smarturl.it/DeadOrAlive_Spotify Listen on Apple Music - http://smarturl.it/DeadOrAlive_AppleMus Amazon - http://smarturl.it/DeadOrAlive_Amazon Lyrics: [Verse 1] If I, I get to know you
From playlist Music [Easy]
Ex: Rounding to the Nearest Ten - Number Line / Formal Rules
This video explains how to round using a number line and using formal rules. http://mathispower4u.com
From playlist Number Sense - Whole Numbers
Estimating Multiplication and Division Problems Involving Whole Numbers
This video explains how to round whole numbers to estimate multiplication and division problems. http://mathispower4u.yolasite.com/
From playlist Whole Number Operations
Ex: Rounding to the Nearest Hundred - Number Line / Formal Rules
This video explains how to round using a number line and using formal rules. http://mathispower4u.com
From playlist Number Sense - Whole Numbers