Download Understanding and Working with Decimals

Understanding and Working with Decimals
The word decimal comes from Latin, and means “of tens” or “tenths.” Each decimal place signifies a
multiple of 10 (with the exception of the units (or ones), which include the numbers 1-9).
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Therefore, multiplying and dividing by tens can be done very easily (which is why the metric system is
favorable in many cases, because it is based on a system of 10s).
Part A
Each time you multiply a number by 10, the decimal point is moved one place to the right. Anytime you
divide by 10, the decimal point is moved one place to the left. When you multiply or divide by multiples
of ten, the same rules apply; you simply move the decimal point the number of places left or right that
equals the number of zeroes you have, adding extra zeroes when necessary.
Example:
0.495 x 10
=
0.495 x 100 =
0.495 x 1000 =
0.495 x 10000 =
4.95
49.5
495
4950
31.2 ÷ 10
31.2 ÷ 100
31.2 ÷ 1000
=
=
=
3.12
0.312
0.0312
Practice:
1)
1618.48
1000
2)
0.0045 x 10
3)
243
10
4)
1.369
100
5) 0.245 x 1000
6)
411.7
10
7)
3.683 x 10
8)
1386.425
1000
Revised 3/21/12 pe
Part B
Multiplying and dividing by decimals is a little different than multiplying and dividing by tens,
hundreds, etc., yet the concept is very similar. In fact, when multiplying or dividing by decimals, the
results are the reverse of what they would be if multiplying and dividing by multiples of ten. See the
examples below for a demonstration of these ideas.
Example 1:
5023.9
0.01 50.239
50.239
 5023.9
0.01
To solve this problem, it is easiest to simply move the decimal point for both numbers to
the right two (2) places. If you move the decimal point two places to the right, then you
are actually dividing the number 5023.9 by 1, and your answer is 5023.9. This can be
seen as the “reverse” of division by multiples of ten because by dividing by 0.01, you
are actually multiplying by 100.
or
Example 2:
487.3
x 0.1
48.73
or
487.3 x 0.1 = 48.73
To solve multiplication problems involving decimals, you move your decimal point to the
left until you have the same number of places which are represented by all the numbers in
your problem. For instance, since you have one decimal place represented in the number
487.3, and one decimal place represented in the number 0.1, in your answer you must
have two decimal places represented. When multiplying a number by the decimal 0.1, you
are actually dividing by 10.
Practice:
Copy the problem onto another sheet of paper. Show all of your work. Do NOT use a calculator!
9)
945.68
0.001
10)
3214.663
0.1
11)
961005
0.01
12)
3.2809
0.0001
13) 1596.357 x 0.01
14) 569.3 x 0.0001
15) 3.6672 x 0.0001
16) 734169.368 x 0.00001
Now, check the problems with a calculator to make sure you did them correctly.
Revised 3/21/12 pe