# How I can round off it? 0.0505 If it is 0.051 then why ? If it is 0.050 then why . Please let me know reason, Thanks a lot.

Apr 20, 2018

The standard convention is 0.050

Although this is a convention, there is a reason for it.

#### Explanation:

If the number to be rounded off were 0.0504, the rounded off version would obviously have been 0.050. This is because, of the two possibilities here, 0.050 is closer to 0.0504 than 0.051 is.

Similarly, had the number to be rounded had been 0.0506, the rounded off version would have obviously been 0.051.

With 0.0505, both 0.050 and 0.051 are equally close, so there is no proximity based reason to chose one over the other. This is why we have to use an established convention for such a case.

The standard convention is that in such cases the rounding will be done so that the final digit in the rounded off number is even. Since 0 is even while 1 is not, in this case we choose the rounded off number to be 0.050

Why is such a convention used? Let's look at an alternative possibility - let's say we decide to round down all the time. This means that we would consistently underestimate such cases - and over a long run, the errors would tend to add up. The same goes for rounding up, except this time we would be consistently overestimating! Using the "last digit convention " is better in the sense that in the long run we will underestimate roughly as many times as overestimate, and the errors will tend to balance out.

Frankly, this isn't really a big issue in day to day calculations, but can make a difference in situations where thousands of numbers are being handled.

Why does the last digit have to be even? As you might have figured out already, it would have made no difference to the justification if we had adopted the convention that the last digit has to be odd - but we do have to pick one, and by established convention we have chosen even over odd.

One important note - the rounding off has to be done in one go. It is wrong to round off 0.05051 first to 0.0505, and then to 0.050. The rounding to three decimal places is 0.051 in this case.