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Lesson 3 MULTIPLYING AND DIVIDINGBY POWERS OF 10The Meaning of PercentIn this Lesson you will learn to multiply and divide by a power of 10 -- simply by moving the decimal point. For the remainder of the course, this will be a fundamental skill . These are problems that do not require a calculator, and certainly should not be done by the historical written method. In this Lesson, we will answer the following:
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Examples.
Problem. If 5 pounds of sugar cost $2.79, how much will 50 pounds cost? Answer. Since 50 pounds are ten times 5 pounds, they will cost ten times more. Move the decimal point one place right: $27.90. Since money has two decimal digits, we added on a 0. (Lesson 3, Question 8) |
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These example illustrate that, whenever we multiply or divide by a power of 10, the digits do not change Finally, we must see how to divide a whole number by a power of 10. Now in Lesson 1 we saw that when a whole number ends in 0's, we simply take off 0's. (Lesson 1, Question 11) 265,000 ÷ 100 = 2,650 But when a whole number does not end in 0's -- as 265 -- then there are no 0's to chop off |
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Again, as in Lesson 1, consider this array:
As we move down the list -- as we push the digits one place left -- the number has been multiplied by 10, because each next place is worth 10 times more. (As we move from 2.658 to 26.58, we go from 2 ones to 2 tens.) It appears, though, as if the decimal point has shifted one place right, or, with whole numbers, that a 0 has been added on. As we move up the list -- as we push the digits to the right -- each number has been divided by 10. And so we can easily multiply or divide by a power of 10 because of the written system itself. Each place belongs to the next power of 10. At this point, please "turn" the page and do some Problems. or Continue on to the Section 2: The meaning of percent. Introduction | Home | Table of Contents Please make a donation to keep TheMathPage online. Copyright © 2001-2009 Lawrence Spector Questions or comments? E-mail: themathpage@nyc.rr.com |
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