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Rounding Decimals


Date: 10/19/98 at 21:56:18
From: Pam Martin
Subject: Rounding decimals

I am trying to teach my daughter how to round decimals. It has been a 
long time since I have done it. Could you please explain how to round 
them in a simple way that I can make her understand?

Thank you,
Pam Martin


Date: 10/20/98 at 13:13:42
From: Doctor Peterson
Subject: Re: Rounding decimals

Hi, Pam. Let's see if I can help.

The first thing to know about rounding decimals is that it works 
exactly like rounding whole numbers. To round to the nearest tenth, you 
do the same thing you do to round to the nearest ten, except that you 
are working with a different digit in the number. I can use the same 
picture to explain both:

    |                        |              X-------->|
    +----+----+----+----+----+----+----+----+----+----+
   140  141  142  143  144  145  146  147  148  149  150


This shows that 148 is between 140 and 150, and is closer to 150 
because it's bigger than 145. The next picture shows that 1.48 is 
between 1.40 and 1.50, and is closer to 1.50 because it is bigger than 
1.45:

    |                        |              X-------->|
    +----+----+----+----+----+----+----+----+----+----+
   1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.50


To round to the nearest ten, you drop all digits to the right of the 
tens place, replacing them with zero, so that you are left with a 
multiple of 10. Then you check to see whether your original number is 
actually nearer to the next multiple of 10, by checking whether the 
next digit (the leftmost one you dropped) was 5 or more:

    148 rounded to nearest 10:
      |\
      | \ replace 8 with 0
      V  \
    140   8 is greater than 5, so add 10:
     |
     |
     V
    150

What all this means is that 148 is between 140 and 150, but is closer 
to 150 so we round it to that.

Now, to round to the nearest tenth, you do the same thing, but using 
the tenths digit rather than the tens:

    1.48 rounded to nearest 0.1:
       |\
       | \ replace 8 with 0
       V  \
    1.40   8 is greater than 5, so add 0.1:
      |
      |
      V
    1.50

Again, this means that 1.48 is between 1.4 and 1.5, but is closer to 
1.5. If the number had been 1.45, exactly between the two, you would 
still round up to 1.5. If it were 1.43, you would have rounded down, 
leaving it at 1.40, because 3 is less than 5.

The only real difference is that when you put zeroes to the right of a 
decimal, you can ignore them completely because they don't affect the 
number. So you can write the answer as 1.5 rather than 1.50.

Here's another answer in our Dr. Math archives that talks about 
rounding decimals:

 http://mathforum.org/library/drmath/view/58938.html   

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
Elementary Fractions
Elementary Place Value

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