Basic Math and Pre-Algebra For Dummies (54 page)

Notice that I again drop the final zero in the decimal 0.1, but I keep the zeros in the decimals 0.05 and 0.01. You can drop zeros from the right end of a decimal, but you can't drop zeros that fall between the decimal point and another digit.

Decimals are just as good for cutting up cake as for cutting up money. Figure 
11-4
gives you a look at the four cut-up cakes that I show you in Chapter
9
. This time, I give you the decimals that tell you how much cake you have. Fractions and decimals accomplish the same task: allowing you to cut a whole object into pieces and talk about how much you have.

In Chapter
2
, you find out about the place value of whole numbers. Table 
11-1
shows how the whole number 4,672 breaks down in terms of place value.

This number means 4,000 + 600 + 70 + 2.

With decimals, this idea is extended. First, a decimal point is placed to the right of the ones place in a whole number. Then more numbers are appended to the right of the decimal point.

For example, the decimal 4,672.389 breaks down as shown in Table 
11-2
.

This decimal means
.

The connection between fractions and decimals becomes obvious when you look at place value. Decimals really are a shorthand notation for fractions. You can represent any fraction as a decimal.

When you understand how place value works in decimals (as I explain in the preceding section), a whole lot of facts about decimals begin to make sense. Two key ideas are trailing zeros and what happens when you move a decimal point left or right.

You probably know that you can attach zeros to the beginning of a whole number without changing its value. For example, these three numbers are all equal in value:

• 27 027 0,000,027
  

The reason becomes clear when you know about place value of whole numbers. See Table 
11-3
.

As you can see, 0,000,027 simply means 0 + 0 + 0 + 0 + 0 + 20 + 7. No matter how many zeros you add to the beginning of a number, the number 27 doesn't change.

Zeros attached to the beginning of a number in this way are called
leading zeros.

In decimals, this idea of zeros that don't add value to a number can be extended to trailing zeros.

 A
trailing zero
is any zero that appears to the right of both the decimal point and every digit other than zero.

For example:

• 34.8 34.80 34.8000
  

All three of these numbers are the same. The reason becomes clear when you understand how place value works in decimals. See Table 
11-4
.

In this example, 34.8000 means
.

 You can attach or remove as many trailing zeros as you want without changing the value of a number.

When you understand trailing zeros, you can see that every whole number can easily be changed to a decimal. Just attach a decimal point and a 0 to the end of it. For example: