Multiplying by a Decimal Number
Date: 02/28/2001 at 14:34:14 From: Carolyn Trancovich Subject: Multiplication of decimal numbers I am having trouble understanding why multiplying by decimal numbers gives a product smaller than the factors. For example, 5 * .43 = 2.15. I just always thought that multiplying would make the product bigger than the numbers I used. Thank you.
Date: 02/28/2001 at 16:49:42 From: Doctor Rick Subject: Re: Multiplication of decimal numbers Hi, Carolyn. When you only knew about whole numbers, you could make a rule like the one you stated - but not quite! Even when you only knew about whole numbers, there was one exception to your rule: multiplying by 1 does not make a number bigger. When you added zero, that was another exception. If you multiply by a number greater than 1, the product will be greater than what you started with. If you multiply by 1, the product is the same as what you started with. If you multiply by a number less than 1, the product is less than what you started with. Let's make some sense of this by considering a simple example. Multiplying by 1/2 is the same as dividing by 2. Do you understand this? Multiplying by 1/2 means taking half of it; dividing by 2 means cutting it in two pieces and keeping one. These amount to the same thing. Since 1/2 = 0.5, and half of something is less than the whole, it makes sense that multiplying a number by 0.5 makes it smaller. You've asked a good question, and others have wondered about it, too. Here are some answers I have written to other students on this topic: Multiplying Decimals and Decreasing Answers http://mathforum.org/dr.math/problems/graham12.2.98.html Multiplying by 1 http://mathforum.org/dr.math/problems/abbasi9.1.98.html - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
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