Basic rounding query

[escribblings]

This seems a silly question to ask, but it has me stumped.

I fully understand the process of rounding down on 0-4 and up on 0.5, so if rounding to 1 decimal place the following would be -

1.00 = 1.0
1.01 = 1.0
1.02 = 1.0
1.03 = 1.0
1.04 = 1.0
1.05 = 1.1
1.06 = 1.1
1.07 = 1.1
1.08 = 1.1
1.09 = 1.1
1.10 = 1.1

The problem I have is with rounding long decimals to short.

Take for example 1.12345

If I were t round to 4 decimal places that would be 1.1235, this I agree with.

My conflict comes if I want to round to 3 decimal places. If it were 1.1234, it would round to 1.123. But it is 1.12345 - now some sites say only to take notice of the number immediately to the right of the last decimal place that you are rounding to - which means 1.12345 rounds to 1.123. But then others round right to left until you get to the require number of decimal places, which means 1.12345 becomes 1.1235 which in turn becomes 1.124.

so, rounding 1.12345 to 3 decimal places, which is correct (and why?)

1.123

or

1.124

Thank you.

 

[Ishuda]

As I have always understood it, the general idea behind rounding a number x to a number y is to make the smallest 'error' in the value of y. In the case of your example of rounding 1.12345 to three decimal we want the number to three decimal places closest to 1.12345. That is 1.123 is in error by 0.00045 and 1.124 is in error by 0.00055 so y is 1.123. That is equivalent to the 'only to take notice of the number immediately to the right' process. Oh, and when it's a tie, go with the larger number.

 

[escribblings]

As I have always understood it, the general idea behind rounding a number x to a number y is to make the smallest 'error' in the value of y. In the case of your example of rounding 1.12345 to three decimal we want the number to three decimal places closest to 1.12345. That is 1.123 is in error by 0.00045 and 1.124 is in error by 0.00055 so y is 1.123. That is equivalent to the 'only to take notice of the number immediately to the right' process. Oh, and when it's a tie, go with the larger number.

Thank you.

That makes perfect sense now I look at it in that way.

I will accept this answer unless anyone wants to argue otherwise.

 

[lookagain]

But then > > > others < < < round right to left until you get to the require number of decimal places, which means 1.12345 becomes 1.1235 which in turn becomes 1.124.

escribblings,

please name one of these alleged sites. Post their web address so I can
verify what you allege. What you are describing that they are touting is
the "error of successive rounding."