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Decimals on the Right

We've covered the basics of decimals in the numbers section. You might also want to look at decimal addition for ideas to help solve these problems faster. You will also learn how to keep decimal points lined up when doing problems. In multiplication, you don't have to worry about lining up the points anymore. You figure out the location of your decimal point when the multiplication problem is over.

No More Line-up

If you can multiply two and three-digit numbers, you can already multiply decimals. Remember when you wrote in some zeros on decimals to make them line up? You don't have to do that anymore either. Let's look at a simple problem...

14.32 x 0.21 1432 + 28640 3.0072

Start by looking at the whole problem. You have simple multiplication. You added a zero when you started to multiply values from the tens column. You added up both of your answers to get the final answer. What about the decimal point? When you figure out the final answer in decimal addition, you need to count the number of places after the decimal points in your factors. In this example, 14.32 has two places after the decimal point and 0.21 has two places after the point. You have a total of four places after the decimal point. When you're done with the numbers, count four places to the left and put that point in there. Our answer was 30072, but when we added the point, the final product was 3.0072. See how there are four places after the decimal point in your answer?

Example:

0.833 x 0.3 ???

(1) Solve the multiplication problem: 833 * 3 = 2499
(2) Count the total number of places after the decimal in the factors: four places.
(3) Write the new decimal point four places to the left on your answer.
Answer: 0.2499

When you work with decimals and the metric system, it's nice to write that first zero in the answer so the reader knows the value is less than one. It's just easier to read than starting the number with a dot.

The Metric System

Decimals are the core of the metric system that is used in science. We introduce ideas about metric measurements in the numbers section. Let's look at one example using measurements a scientist might use...

You need a certain amount of a chemical for your experiment. You have five test tubes that need 0.65 grams of the compound in each tube. How much do you need in total?

5 test tubes * 0.65 grams each = Total grams needed

5 x 0.65 = ?
-or-

0.65 x 5 3.25

You will need 3.25 grams of the compound to conduct the experiment. (We came up with an answer and then added the decimal point two places in.)

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