Interpreting What "Rounding Up" Means

Date: 11/25/2006 at 15:35:20
From: Ariana
Subject: Rounding up to nearest hundred

What is the rule for rounding a multiple of 100 up to the nearest 
hundred?  For example, does 400, rounded up to the nearest hundred, 
round to 400 or 500?

If I am rounding up, it must be to the higher number but my mom thinks 
it's not.  I think 400 has to go up to 500 because if you round up, it 
has to round to a higher number.  I know 400.00000001 would round up 
to 500.  But my mom thinks it is different for 400.00000001 and 400.

Date: 11/25/2006 at 17:23:38
From: Doctor Rick
Subject: Re: Rounding up to nearest hundred

Hi, Ariana.

I understand your thinking.  But for the purposes of rounding, we 
consider the "next" multiple of 100 to be the number you're at, if 
it's already a multiple of 100.  We don't have to go "up" all the 
time because we're rounding "up"; we just make sure we don't go down!

Why?  Well, think about how you'll be using this concept of "rounding 
up".  Say I've got to buy greeting cards for 624 friends and 
relatives, and I can only buy them in packages of 100.  How many 
boxes do I have to buy?  One way to solve this problem is to round up 
to the next multiple of 100: that's 700, requiring 700/100 = 7 boxes.

But what if I've got 400 friends and relatives?  Do I need to buy 5 
boxes?  No, 4 boxes are enough (in fact, exactly enough).  If rounding 
up to the nearest multiple of 100 is going to give the best solution 
to my problem no matter how many friends I have, we need to define it 
so that 400 rounds to 400, not 500.

The moral of this story is that even in math, we don't define things 
rigidly, based just on the meanings of the words we're using.  We 
think about what definition will be most useful to us!  If we're not 
going to use the concept of rounding up, there is no point in defining 
it at all.

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

Date: 12/08/2006 at 13:16:05
From: Ariana
Subject: Thank you (Rounding up to nearest hundred)

Hi, you responded to a question my daughter had about rounding.  She
did not expect a response and was absolutely thrilled that you 
answered her question, and so quickly!  She does not always get 
positive feedback about her mathematical interest and ability so this
really made her day.  Whoever you people are who keep Dr. Math going,
we appreciate you and wish you the best!  

- Mary, Ariana's mom