Basic Math and Pre-Algebra For Dummies (56 page)

To round a decimal to two decimal places, focus on the second and third decimal places (that is, the hundredths and thousandths places):

Everything you already know about adding, subtracting, multiplying, and dividing whole numbers (see Chapter
3
) carries over when you work with decimals. In fact, in each case, there's really only one key difference: how to handle that pesky little decimal point. In this section, I show you how to perform the Big Four math operations with decimals.

The most common use of adding and subtracting decimals is working with money — for example, balancing your checkbook. Later in this book, you find that multiplying and dividing by decimals is useful for calculating percentages (see Chapter
12
), using scientific notation (see Chapter
14
), and measuring with the metric system (see Chapter
15
).

Adding decimals is almost as easy as adding whole numbers. As long as you set up the problem correctly, you're in good shape. To add decimals, follow these steps:

1. Arrange the numbers in a column and line up the decimal points vertically.
   
2. Add as usual, column by column, from right to left.
   
3. Place the decimal point in the answer in line with the other decimal points in the problem.
   

For example, suppose you want to add the numbers 14.5 and 1.89. Line up the decimal points neatly, as follows:

Begin adding from the right-most column. Treat the blank space after 14.5 as a 0 — you can write this in as a trailing 0 (see earlier in this chapter to see why adding zeros to the end of a decimal doesn't change its value). Adding this column gives you 0 + 9 = 9:

Continuing to the left, 5 + 8 = 13, so put down the 3 and carry the 1:

Complete the problem column by column, and at the end, put the decimal point directly below the others in the problem:

When adding more than one decimal, the same rules apply. For example, suppose you want to add 15.1 + 0.005 + 800 + 1.2345. The most important idea is lining up the decimal points correctly:

 To avoid mistakes, be especially neat when adding a lot of decimals.

Because the number 800 isn't a decimal, I place a decimal point and a 0 at the end of it, to be clear about how to line it up. If you like, you can make sure all numbers have the same number of decimal places (in this case, four) by adding trailing zeros. When you properly set up the problem, the addition is no more difficult than in any other addition problem:

Subtracting decimals uses the same trick as adding them (which I talk about in the preceding section). Here's how you subtract decimals:

1. Arrange the numbers in a column and line up the decimal points.
   
2. Subtract as usual, column by column from right to left.
   
3. When you're done, place the decimal point in the answer in line with the other decimal points in the problem.
   

For example, suppose you want to figure out 144.87 – 0.321. First, line up the decimal points:

In this case, I add a zero at the end of the first decimal. This placeholder reminds you that, in the right-most column, you need to borrow to get the answer to 0 – 1:

The rest of the problem is straightforward. Just finish the subtraction and drop the decimal point straight down: