Hidden Decimal Points

Date: 02/04/2002 at 17:25:02
From: Michael
Subject: Subtracting Whole Numbers from a Decimal

I get confused when subtracting 4 from 24.98. I keep coming up with  
24.94. Could you explain why whole numbers do not show their decimal 
point?

Date: 02/04/2002 at 23:00:14
From: Doctor Peterson
Subject: Re: Subtracting Whole Numbers from a Decimal

Hi, Michael.

The first thing to do is to keep in mind, as you are aware, that the 
decimal point of a whole number is hidden to the right of the number. 
Why? Because in a whole number like 24, the rightmost digit is always 
the ones place; when we add tenth and hundredths, and so on, to the 
right of it, we need to mark where the ones place is. So we use a 
decimal point to separate the whole part from the fractional part, and 
the units place is just to the left. Whole numbers don't show it, 
simply because it's not necessary, and we don't like to waste ink. (It 
can also look confusing, as in my next sentence.)

But we CAN show it; here we want to subtract 4. from 24.98. When you 
subtract whole numbers, you line up corresponding places by lining up 
the right side, so that you subtract ones from ones, tens from tens, 
and so on. With decimals, you do the same thing, but you do it by 
lining up the decimal points. That means we have to subtract

      24.98
    -  4.
    -------

Now we are subtracting 4 ones from 4 ones, not 4 ones from 8 
hundredths, which wouldn't make sense.

To make it clearer, we can now fill in the empty places with zeros if 
it makes you feel better:

      24.98
    -  4.00
    -------

Now just do the subtraction as if the decimal points weren't there:

      24.98
    -  4.00
    -------
      20.98

There's the answer. The only trick is lining up the decimal points, as 
if they were holes you put a pin through to hold everything in place. 
Where the pin pokes through the bottom, you put a decimal point in the 
answer.

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