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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). 1 2 3 4 t h o u s a n d s h u n d r e d s t e n s o n e s . 5 6 7 t e n t h s h u n d r e d t h s t h o u s a n d t h s 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