Multiplying Decimal Numbers and Placing the Decimal Point
Date: 09/20/2007 at 10:38:39 From: tel Subject: Multiply numbers with fractions. When I multiply something like 24.5 x 36.7, I get the decimal point in the wrong place. 24.5 36.7 -------- 171.5 1470.0 7350.0 ------- 8991.5 answer is 899.15 - get decimal point wrong ....
Date: 09/20/2007 at 11:50:17 From: Doctor Ian Subject: Re: Multiply numbers with fractions. Hi Tel, I like to work with integers, so I usually change decimals to fractions when I want to multiply or divide: 2.57 * 2.63 257 263 257 * 263 = --- * --- = --------- 100 100 10,000 Now I can do the multiplication on top without worrying about decimal points: 257 * 263 ----- 771 <- 3 * 257 15420 <- 60 * 257 51400 <- 200 * 257 ----- 67591 to get 67,591 ------ 10,000 And that means the same thing as 6.7591 As a quick check, note that I've got 2 point something * 2 point something so the answer should be a little bigger than 4. This can be a good way to make sure you didn't slide a decimal point too far, or not far enough! If I end up with something like 67, I can see right away that's too big; similarly, something like 0.67 would be too small. Anyway, the moral is that being able to go back and forth between decimal and fraction notations is a big advantage, both in being able to explain WHY various decimal operations work the way they do, and in being able to AVOID lots of complicated operations entirely, by working with integers. Does that make sense? Try your problem this way, and please let me know how it works out for you. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 09/20/2007 at 12:04:17 From: tel Subject: Thank you (Multiply numbers with fractions.) Got it - a good way to simplify. Thanks. I am sure I used to do it with the decimal point and putting a zero, then 2 zero's - etc... or am I making it up? Regards T
Date: 09/20/2007 at 12:17:16 From: Doctor Ian Subject: Re: Thank you (Multiply numbers with fractions.) Hi Tel, The usual way of doing it is to 1. Count up the total number of decimal places. 2. Forget about them, and multiply as if you just have integers. 3. 'Put back' the number of decimal places you found in step (1). Do you see why it amounts to the same thing? We're doing step (1) when we convert to fraction notation and multiply the denominators. We're doing step (2) when we multiply the numerators. We're doing step (3) when we convert back to decimal notation. Once you know what's going on, it's quicker to do the multiplication without explicitly constructing the fractions. But the fraction method is always there as a backup. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 09/20/2007 at 12:19:51 From: tel Subject: Thank you (Multiply numbers with fractions.) Even clearer - many thanks indeed!
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