Rounding to the Nearest Tenth

Date: 08/29/98 at 22:26:00
From: Anonymous
Subject: Algebra 1

I love all math and have always made very good grades in math, but I've 
run into a problem. As part of a review, my (new) Algebra teacher 
wanted us to round some numbers. One such number was 6.96, which we 
were to round to the nearest tenth. I said 7.0, as did most of my 
classmates. Our teacher said this was wrong, that it is 6.9. We asked 
her to please double-check this and she still insisted that it was 6.9. 
She said she checked it on her calculator. I am confused. Is there any 
instance in which 6.96 rounded to the nearest tenth would be 6.9?  This 
is not what I learned in previous years. I don't mind that she counted 
the answer wrong, I mind that I don't know why.

Thank you for being there.

Date: 08/31/98 at 16:59:52
From: Doctor Peterson
Subject: Re: Algebra 1

Hi. Congratulations for being confident enough to get confused 
by this, and not just accept what the teacher said. I'm confused too.

Of course you are right, the answer is 7.0. To prove it, you could 
just draw a number line:

        6.90                                             7.00
   6.89  |   6.91 6.92 6.93 6.94 6.95 6.96 6.97 6.98 6.99  |  7.01
    +----+----+----+----+----+----+----+----+----+----+----+----+
                                        |
                                        +------------------->
                                            nearest tenth

Another way to think about it is to change the problem from rounding 
6.96 to the nearest tenth to rounding 69.6 to the nearest integer, 
which ought to have the equivalent answer, 70.0.

What puzzles me, like you, is what the teacher can be doing wrong. I 
can't think of any different definition she could be using, unless the 
problem was to round down to the nearest integer, which I doubt. I 
don't have a calculator with a "round" key, if that's what your teacher 
used, so I don't know what quirks it might have, such as always 
rounding down. The only mistake I can picture would be to round to the 
nearest integer rather than tenth, but that would give your answer. 
It's easy to get confused in a problem like this, where rounding up 
changes the whole number.

- Doctor Peterson, The Math Forum
Check out our web site! http://mathforum.org/dr.math/