Dividing and Rounding

Date: 08/23/2001 at 20:41:40
From: Britt
Subject: Dividing and rounding

I have to answer a division problem and then round the quotient to 
the nearest hundredth. The problem is: 

6 divided by 312.8

I solved and got 52.13. Now I have to round it to the nearest 
hundredth. What do I do?

Britt

Date: 08/23/2001 at 22:53:30
From: Doctor Peterson
Subject: Re: Dividing and rounding

Hi, Britt.

First, let's correct your terminology. You didn't divide 6 by 312.8; 
you divided 312.8 by 6. A lot of students say it backward because we 
write the divisor on the left when we do the work.

Your answer really isn't exactly 52.13; if it were, you would be done, 
because there's no rounding to do. Because you had a remainder, you 
should have kept going for another digit; you would get 52.133. In 
fact, the answer is exactly 52.13333..., where the 3's keep going 
forever.

Now that you have an extra digit, you have something to round off. If 
it had been 5 or more, you would have to round up to 52.14; but since 
it is a 3, your answer of 52.13 turns out to be correct.

Here's the key to this kind of question: go one digit beyond the 
number you need to end up with, and then round off that last digit. 
That ensures that whatever remainder you would have had "has its say," 
by forcing you to round in the right direction. Then your answer is 
correct to the nearest hundredth.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/