Basic Math and Pre-Algebra For Dummies (55 page)

 Make sure that you don't attach or remove any nonleading or nontrailing zeros — it changes the value of the decimal.

For example, look at this number:

• 0450.0070
  

In this number, you can remove the leading and trailing zeros without changing the value, as follows:

• 450.007
  

The remaining zeros, however, need to stay where they are as
placeholders
between the decimal point and digits other than zero. See Table 
11-5
.

I continue to discuss zeros as placeholders in the next section.

When you're working with whole numbers, you can multiply any number by 10 just by adding a zero to the end of it. For example:

To see why this answer is so, again think about the place value of digits and look at Table 
11-6
.

Here's what these two numbers really mean:

As you can see, that little zero makes a big difference: It causes the rest of the numbers to shift one place.

This concept makes even more sense when you think about the decimal point. See Table 
11-7
.

In effect, adding a 0 to the end of a whole number moves the decimal point one place to the right. So for any decimal, when you move the decimal point one place to the right, you multiply that number by 10. This fact becomes clear when you start with a simple number like 7:

In this case, the net effect is that you moved the decimal point three places to the right, which is the same as multiplying 7 by 1,000.

Similarly, to divide any number by 10, move the decimal point one place to the left. For example:

• 7.0
  
• 0.7
  
• 0.07
  
• 0.007
  

This time, the net effect is that you moved the decimal point three places to the left, which is the same as dividing 7 by 1,000.

Rounding decimals works almost exactly the same as rounding numbers. You'll use this skill when dividing decimals later in the chapter. Most commonly, you need to round a decimal either to a whole number or to one or two decimal places.

To round a decimal to a whole number, focus on the ones digit and the tenths digit. Round the decimal either up or down to the
nearest
whole number, dropping the decimal point:

When the tenths digit is 5, round the decimal
up
:

If the decimal has other decimal digits, just drop them:

Occasionally, a small change to the ones digit affects the other digits. (This example may remind you of when the odometer in your car rolls a bunch of 9s over to 0s):

The same basic idea applies to rounding a decimal to any number of places. For example, to round a decimal to one decimal place, focus on the first and second decimal places (that is, the tenths and hundredths places):