Pre Algebra Approximation
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Take a Good Guess
Approximation

 
 Sometimes it would be nice if we had a quick way 
 to get a number that was very close to the right answer.
 

WE DO!

 
 This is a trick that is mostly used with multiplying, 
 but can really be used anywhere.
 Say you want to know about how much you get 
 when you multiply 48 times 32.
 

 
 We COULD work this out, 
 but watch this. 
 48 is close to 50. 
 32 is close to 30. 
 If we multiplied 50 times 30 we would get a number
 that was close to the answer of 48 times 32.
 
 That's pretty good, but we can make it easier.
 
 50 is just a 5 in the tens column.
 30 is just a 3 in the tens column.
 
 If we multiply 5 times 3 we will get about the right number
 except for the number of zeros we need in the answer.
 

5 x 3 = 15

 
 Now what about those zeros?
 
 Here's how it works. 

50 has one zero.  

 30 has one zero.
 That's 2 zeros, 
 and that's how many go in the answer.
 
 So our guess is 1500. 
 
 The real answer when we multiply 48 times 32 is 1536. 
 Our guess was off by less than 3 percent.
 
 Try another one ...
 
 Example:
 

 
 615 is close to 600 
 491 is close to 500
 

6 x 5 = 30

 
 The numbers had a total of 4 zeros in them 
 so add 4 zeros to the 30. 
 You get:

300,000

 
 The real answer to 615 x 491 is 301,965.
 Not to bad, eh?
 
 If you need to solve any problem, 
 you should go ahead and use this trick first. 
 
 Then you will know about what the answer should be. 
 If you get something that's WAY different, 
 you will know that you made a mistake somewhere. 
 That type of mistake happens a lot when people use calculators. 
 Calculators don't make mistakes when they do math. 
 But if you hit a wrong key, 
 the calculator will very nicely calculate the wrong answer.
 

   copyright 2005 Bruce Kirkpatrick

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