Rounding to the Nearest...

Date: 10/15/97 at 18:10:12
From: Elizabeth Petersen
Subject: Rounding to the nearest

I don't get rounding to the nearest! I don't know if you're supposed 
to round a number (say 451.7576) to 451 or 451.7 or 451.8 when my 
teacher tells me to round to the nearest tenth. It's so confusing!

Date: 10/15/97 at 19:02:59
From: Doctor Keith
Subject: Re: Rounding to the nearest

Hi there!

Great question! 

We always want to keep two things in mind when we round any number. 
The first is what we are rounding to. In your example we are rounding 
to tenths, so we should end up with one digit to the right of the 
decimal point, because that is the tenths place. Now immediately you 
can see that 451 is not an acceptable answer, but 451.7 or 451.8 
could be.

The second thing to keep in mind is the method we are using to round
by. In your problem that is the nearest method. In the nearest method
we look at the digit to the immediate right of the digit we will round
to (so for this example we will look at the hundredths digit), and if
it is a five or greater (5 through 9) we round up (add 1 to the digit 
we are rounding and drop all the digits to the right). If the digit 
to the right of our rounding digit is less than 5 (0 through 4) we 
round down (drop all digits to the right of digit we are rounding).

So for our example:

  number to be rounded to nearest tenth      451.7576  
  number to the right of the tenths digit    5
  since the number is a 5 we round up        451.8

  so our answer is 451.8

What if we had 451.7476 instead?

  number to be rounded to nearest tenth      451.7476  
  number to the right of the tenths digit    4
  since the number is a 4 we round down      451.7

  so our answer is 451.7

How about rounding 451.7576 to the nearest hundredth?

  number to be rounded to nearest hundredth      451.7576  
  number to the right of the hundredths digit    7
  since the number is a 7 we round up            451.76

  so our answer is 451.76

Now you try: (solutions below)

  a) round 72.3478 to the nearest tenth
  b) round 15.4201 to the nearest tenth
  c) round 5.74999 to the nearest tenth
  d) round 87.5555 to the nearest hundredth

I hope this is a bit clearer now. If anything was not clear in my 
explanation, just write back noting what was confusing, and I will try 
to make it clearer. To check your work, here are the answers to the 
questions above: 

  a) 72.3 
  b) 15.4
  c) 5.7
  d) 87.56 .  

I hope that you have more fun in class!  Good luck,

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