[Wissarut]

I am very confused how to rounding off for significant value.

If I want to rounding off the value  0.0575001,

which value I should get between 0.0575 or 0.0585 ?

(When the next digit from 5 is Zero and then what is the next step to consider??)

Help me please...Best regards.

PS. I'm so sorry, my English language is not good. If anyone don't understand, you can ask me again.  

[Borek]

0.0575

Why do you think 0.0585? Rounding can change only the last digit, not some digit in the middle.

And the simplest rule is - if the next digit is 5 or more (5,6,7,8,9) round up, if it is 4 or less (4,3,2,1,0) don't change. So

0.40 -> 0.4
0.41 -> 0.4
0.42 -> 0.4
0.43 -> 0.4
0.44 -> 0.4
0.45 -> 0.5
0.46 -> 0.5
0.47 -> 0.5
0.48 -> 0.5
0.49 -> 0.5

Any further digits are just ignored, so there is no difference between 0.411 and 0.419.

There are also some more elaborate systems, but they are rarely used and not worth your attention.

[Wissarut]

I'm so sorry.
I wrote wrong selection.

Please choose again between 0.057 or 0.058.

[DrCMS]

Borek  has already given the correct way to do it - the correct value would be 0.058.

[Wissarut]

Thank you so much Borek and DrCMS. 

and the rule "when there are no digit following 5, Increment by 1 or remaining the number depend on that digit is odd or even." should be concerned too. Right? or it is not neccessary.

I almost understand it. Please answer to me 

[Borek]

and the rule "when there are no digit following 5, Increment by 1 or remaining the number depend on that digit is odd or even." should be concerned too. Right? or it is not neccessary.

It helps when you need to sum those rounded numbers later. Standard rule (that doesn't care about whether the digit is odd or even) introduces a systematic positive error.

But it matters so rarely I never cared.

[Wissarut]

Thank you for your advices Borek.

All answers are helpful for my work.

Best regards 

[fledarmus]

Thank you so much Borek and DrCMS. 

and the rule "when there are no digit following 5, Increment by 1 or remaining the number depend on that digit is odd or even." should be concerned too. Right? or it is not neccessary.

I almost understand it. Please answer to me 

This is one of those slightly more elaborate systems that Borek mentioned. As Wissarut said, it is intended to prevent a slightly positive creep in the rounding errors, but with the advent of calculaters and computers that can keep track of large numbers of digits without all the rounding errors in the intermediates that were normal in the days of slide rules, it almost isn't worth the effort anymore. Easier to just carry all the digits through the calculation and round at the end.

[billnotgatez]

Easier to just carry all the digits through the calculation and round at the end.

I think that might get you an incorrect answer on an exam
but it is what I do in real life

 

[Wissarut]

For my work, I have to write the document (call WI or working intruction), so I want the obvious and right method to do.

In addition to my work, error is the point I must concern seriously.
(This is just my opinion.)

To minimize systemic error is what I should do.