Please help me with rounding!

[ambia]

I have always been taught that if it's 1-4 you round down, and 5-9 you round up, however my Calculus teacher recently gave us the opportunity for extra credit by finding the "proper" way to round. Apparently it deals with rounding the 5 and whether it rounds up or down. I have found many different ways to round; even, odd etc. But none of them say that they are the correct way.
Does anyone have any ideas? I'd really appreciate it!

 

[mmm4444bot]

You typed quotation marks around the word "proper".

Did your teacher do that, too?

Different branches of learning may have different rounding methods. A method that is proper for one group may not be considered proper by another group (eg: statisticians, engineers, bankers, chemists).

Perhaps, you will get the extra credit by simply describing for your teacher a few of these methods, along with who uses them and why.

 

[soroban]

Hello, ambia!

I have always been taught that if it's 1-4 you round down, and 5-9 you round up.

I'm convinced that that is the "fair" way of rounding.

Consider a number of the form \(\displaystyle 17.d\) . where \(\displaystyle d\) is a digit.

There are 10 choices for the digit \(\displaystyle d.\)
. . In half of them \(\displaystyle \{0,1,2,3,4\}\), we round down.
. . In half of them \(\displaystyle \{5,6,7,8,9\}\), we round up.

Can it be more fair?