Rounding Decimals

Date: 06/14/99 at 10:40:58
From: Ken Ives
Subject: Rounding decimals

This question is based on your answer "Rounding Decimals" at:

  http://mathforum.org/dr.math/problems/martin10.19.98.html   

My number is 1.9949. I want to round to 2 decimal places. Is the 
answer 2.00 or 1.99? I would say 2.00. 

Now if I change the number to 1.99449, is the answer 2.00 or 1.99? 
Starting at the right, 9 raises the 4 to 5; therefore, 5 raises the 
next 4 to 5; the 5 raises the 9 to 10; etc., thus 2.00 is the correct 
answer.

Is this correct or not?  

Thank you in advance for answering.

Date: 06/14/99 at 15:01:36
From: Doctor Terrel
Subject: Re: Rounding decimals

Dear Ken,

A lot of people are unsure about this idea in rounding, when a 4 
occurs in the way you showed with 9's before and after it.

But think of it as which value is something "closer to."

Let's try a smaller, yet similar case: 1.949. Is it 2.0 or 1.9 (to the 
nearest tenth?)

In fraction form, 1.949 = 1 and 949/1000.

Compare this to 1 and 1000/1000 (another form for "2") and 1 and 
900/1000 (which is 1.9 in decimal form). Surely you agree that 
949/1000 is closer to 900/1000 than it is to 1000/1000; it is only 
49/1000 to the lower value, yet 51/1000 to the higher value.

This all lets us condense our work to this simple rule:

If the digit immediately to the right of the place to which we wish to 
round is 5 or greater, then increase the digit in that place by one.

So for your number, 1.99449, to two decimal places it would be 1.99. 
(Check with your calculator's "fix" function to see this happen.)

   to 1 place   ---  2.0
   to 2 places  ---  1.99
   to 3 places  ---  1.994
   to 4 places  ---  1.9945

In other words, we don't start at the far right and "work our way 
over" to the left.

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