Multiplying Decimals and Decreasing Answers
Date: 12/02/98 at 21:32:14 From: Danny Graham Subject: Multiplying decimals I know that when I multiply, .60 * .75 * .80 = .36. But what is the .36 telling me? 36/100. It seems I have less than I had when I started. I read the questions others have asked, and I understand the process of multiplying the decimals, I just don't understand what the answer is telling me. Thank you, Danny Graham
Date: 12/03/98 at 17:57:53 From: Doctor Rick Subject: Re: Multiplying decimals Hi, Danny. I'm impressed - you're really thinking! Multiplication isn't just a set of rules you follow to please the teacher. It's supposed to tell you something. So, what is it telling us? It is surprising indeed that multiplication can give you a smaller number than you started with. One student from a foreign country got really upset at this - his foreign-language dictionary told him that "multiply" is a synonym for "increase," so how can it make numbers decrease? Numbers decrease when you multiply by a number less than one. It works the same with fractions as with decimals. For instance, if you multiply any (positive) number by 1/2, the answer is less than you started with. Let's rewrite your decimal multiplication problem as fractions: .60 * .75 * .80 = .36 3 3 4 9 --- * --- * --- = --- 5 4 5 25 The answer comes out the same, if you work it out: 9/25 = 0.36. The only new thing is that it is much easier to see that 0.36 < 0.60 than it is to see that 9/25 < 3/5. (It is: 3/5 = 15/25, and 9 < 15.) Multiplying by a decimal less than 1 will always decrease a number. Multiplying by 0.75 is the same as multiplying by 3/4, and 3/4 of something is always less than 4/4 of it, which is the whole thing. I hope this helps you to see what is going on. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
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