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” in this segment. We re going to talk about round off errors. There there are several possibilities of error. Whenever you re going to use numerical methods.

But want to concentrate here on just two errors. One is the round off error and the other is the truncation error. So those are the sources of error. Which we are going to talk about because those are the ones.

Which are coming from something on which you may or may not have as much control as other errors like for example. If you have made a mistake in programming or if your logic is wrong those are not the kind of errors..

Which we are talking about when we talk about numerical methods. So you re going to have two sources of error. Which you are going to have one is round off error and. The other one is called truncation error .

And let s go ahead and concentrate on what round off error is now round off error is defined. As. Follows it is basically. The error which comes from .

so error. Created..

Due to approximate representation of numbers . So. The round. Off.

Error is simply the error created by the approximate representation of numbers because in a computer. You ll be able to only represent a number only so approximately for example. If you have a number like 1 divided by 3. And you had a six significant digit computer.

Let s suppose in the. Decimal notation then this..

Can be only approximated as 0333333 . and six there s another 3 here. So you re seeing that already a simple number a simple rational number like 1 divided by 3. Cannot be written exactly in the decimal format.

So the amount of round off error. Which you are getting here is the difference between the value of 1 divided by 3 and the value of. 0333333 so in this. Case this error is.

00000003333 and so on and so forth you re going to get similar round off errors from other numbers also like you may have pi that also cannot be represented exactly even in a decimal format. And then square root of 2 things like that so you re finding out there are many many numbers individual numbers like 1 divided by 3 or pi or square root of 2..

Which cannot be represented exactly in a computer. So that s why this creates the round off error the round off error is the difference between what you want to what you want to be able to approximate of what you want to be able to denote and what you are able to get as its approximation. So that s the that s what we call as round off error so that s. The end of this particular segment here .

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One of sources of error in numerical methods is round off error – error caused by approximating numbers. For more videos and resources on this topic, please visit http://nm.mathforcollege.com/topics/sources_of_error.html

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Round off Error, Sources of error, numerical methods, numericalmethodsguy