Basic Math and Pre-Algebra For Dummies (58 page)

Follow these steps:

1. Change 0.333 into a whole number by moving the decimal point three places to the right; at the same time, move the decimal point in 67.8 three places to the right:
   

   

   In this case, when you move the decimal point in 67.8, you run out of room, so you have to add a couple zeros to the dividend. This step is perfectly valid, and you need to do this whenever the divisor has more decimal places than the dividend.
   

2. Place the decimal point in the quotient directly above where it appears in the dividend:
   

   

3. Divide as usual, being careful to correctly line up the numbers in the quotient. This time, 333 doesn't go into 6 or 67, but it does go into 678 (two times). So place the first digit of the quotient directly above the 8:
   

   

   I've jumped forward in the division to the place where I bring down the first 0. At this point, 333 doesn't go into 120, so you need to put a 0 above the first 0 in 67,800 and bring down the second 0. Now, 333 does go into 1,200, so place the next digit in the answer (3) over the second 0:
   

   

This time, the division doesn't work out evenly. If this were a problem with whole numbers, you'd finish by writing down a remainder of 201. (For more on remainders in division, see Chapter
3
.) But decimals are a different story. The next section explains why, with decimals, the show must go on.

When you're dividing whole numbers, you can complete the problem simply by writing down the remainder. But remainders are
never
allowed in decimal division.

A common way to complete a problem in decimal division is to round off the answer. In most cases, you're instructed to round your answer to the nearest whole number or to one or two decimal places (see earlier in this chapter to find out how to round off decimals).

To complete a decimal division problem by rounding it off, you need to add at least one trailing zero to the dividend:

• To round a decimal to a whole number, add one trailing zero.
  
• To round a decimal to one decimal place, add two trailing zeros.
  
• To round a decimal to two decimal places, add three trailing zeros.
  

Here's what the problem looks like with a trailing zero attached:

Attaching a trailing zero doesn't change a decimal, but it does allow you to bring down one more number, changing 201 into 2,010. Now you can divide 333 into 2,010:

At this point, you can round the answer to the nearest whole number, 204. I give you more practice dividing decimals later in this chapter.

Fractions (see Chapters
9
and
10
) and decimals are similar, in that they both allow you to represent parts of the whole — that is, these numbers fall on the number line
between
whole numbers.

In practice, though, sometimes one of these options is more desirable than the other. For example, calculators love decimals but aren't so crazy about fractions. To use your calculator, you may have to change fractions into decimals.

As another example, some units of measurement (such as inches) use fractions, whereas others (such as meters) use decimals. To change units, you may need to convert between fractions and decimals.

In this section, I show you how to convert back and forth between fractions and decimals. (If you need a refresher on fractions, review Chapters
9
and
10
before proceeding.)

Some decimals are so common that you can memorize how to represent them as fractions. Here's how to convert all the one-place decimals to fractions:

And, here are few more common decimals that translate easily to fractions:

Converting a decimal to a fraction is pretty simple. The only tricky part comes in when you have to reduce the fraction or change it to a mixed number.

In this section, I first show you the easy case, when no further work is necessary. Then I show you the harder case, when you need to tweak the fraction. I also show you a great time-saving trick.

Here's how to convert a decimal to a fraction:

1. Draw a line (fraction bar) under the decimal and place a 1 underneath it.
   

   Suppose you want to turn the decimal 0.3763 into a fraction. Draw a line under 0.3763 and place a 1 underneath it:
   

   

   This number looks like a fraction, but technically it isn't one because the top number (the numerator) is a decimal.
   

2. Move the decimal point one place to the right and add a 0 after the 1.
   

   

3. Repeat Step 2 until the decimal point moves all the way to the right so you can drop the decimal point entirely.
   

   In this case, this is a three-step process:
   

   

   As you can see on the last step, the decimal point in the numerator moves all the way to the end of the number, so dropping the decimal point is okay.
   

   Note:
   Moving a decimal point one place to the right is the same thing as multiplying a number by 10. When you move the decimal point four places in this problem, you're essentially multiplying the 0.3763 and the 1 by 10,000. Notice that the number of digits after the decimal point in the original decimal is equal to the number of 0s that end up following the 1.