Basic Math and Pre-Algebra For Dummies (57 page)

As with addition, the decimal point in the answer goes directly below where it appears in the problem.

Multiplying decimals is different from adding and subtracting them, in that you don't have to worry about lining up the decimal points (see the preceding sections). In fact, the only difference between multiplying whole numbers and decimals comes at the end.

Here's how to multiply decimals:

1. Perform the multiplication as you do for whole numbers.
   
2. When you're done, count the number of digits to the right of the decimal point in each factor, and add the result.
   
3. Place the decimal point in your answer so that your answer has the same number of digits after the decimal point.
   

This process sounds tricky, but multiplying decimals can actually be simpler than adding or subtracting them. Suppose, for instance, that you want to multiply 23.5 by 0.16. The first step is to pretend that you're multiplying numbers without decimal points:

This answer isn't complete, though, because you still need to find out where the decimal point goes in the answer. To do this, notice that 23.5 has one digit after the decimal point and that 0.16 has two digits after the decimal point. Because 1 + 2 = 3, place the decimal point in the answer so that it has three digits after the decimal point. (You can put your pencil at the 0 at the end of 3760 and move the decimal point three places to the left.)

 
Even though the last digit in the answer is a 0, you still need to count this as a digit when placing the decimal point. When the decimal point is in place, you can drop trailing zeros (flip to “Understanding Basic Decimal Stuff,” earlier in this chapter, to see why the zeros at the end of a decimal don't change the value of the number).

So the answer is 3.760, which is equal to 3.76.

Long division has never been a crowd pleaser. Dividing decimals is almost the same as dividing whole numbers, which is why a lot of people don't particularly like dividing decimals, either.

But at least you can take comfort in the fact that, when you know how to do long division (which I cover in Chapter
3
), figuring out how to divide decimals is easy. The main difference comes at the beginning, before you start dividing.

Here's how to divide decimals:

1. Turn the
   divisor
   (the number you're dividing by) into a whole number by moving the decimal point all the way to the right; at the same time, move the decimal point in the
   dividend
   (the number you're dividing) the same number of places to the right.
   

   For example, suppose you want to divide 10.274 by 0.11. Write the problem as usual:
   

   

   Turn 0.11 into a whole number by moving the decimal point in 0.11 two places to the right, giving you 11. At the same time, move the decimal point in 10.274 two places to the right, giving you 1,027.4:
   

   

2. Place a decimal point in the
   quotient
   (the answer) directly above where the decimal point now appears in the dividend.
   

   Here's what this step looks like:
   

   

3. Divide as usual, being careful to line up the quotient properly so that the decimal point falls into place.
   

   To start out, notice that 11 is too large to go into either 1 or 10. However, 11 does go into 102 (nine times). So write the first digit of the quotient just above the 2 and continue:
   

   

   I paused after bringing down the next number, 7. This time, 11 goes into 37 three times. The important point is to place the next digit in the answer just above the 7:
   

   

   I paused after bringing down the next number, 4. Now, 11 goes into 44 four times. Again, be careful to place the next digit in the quotient just above the 4, and complete the division:
   

   

   So the answer is 93.4. As you can see, as long as you're careful when placing the decimal point and the digits, the correct answer appears with the decimal point in the right position.
   

Sometimes you have to add one or more trailing zeros to the dividend. As I discuss earlier in this chapter, you can add as many trailing zeros as you like to a decimal without changing its value. For example, suppose you want to divide 67.8 by 0.333: