Operations in Scientific NotationDate: 08/30/2001 at 22:18:07 From: Caitlin Hannigan Subject: Scientific Notation How do you add, multiply, and divide in scientific notation? Date: 08/31/2001 at 13:12:24 From: Doctor Rick Subject: Re: Scientific Notation Hi, Caitlin. You can read about multiplying numbers in scientific notation in our Dr. Math Archives: Using Scientific Notation http://mathforum.org/dr.math/problems/dud11.1.97.html I'll use nearly the same example: (4.567839 * 10^6) * (5.493711 * 10^4) This can be rewritten as follows: (4.567839 * 5.493711) * (10^6 * 10^4) A product of powers of the same base is the same as the base to the sum of the powers, so we can write: (4.567839 * 5.493711) * (10^(6+4) Do the multiplication and addition: 25.094387 * 10^10 This isn't quite scientific notation because the numeric part isn't in the range 1 to 10. To make it so, we divide the numeric part by 10, and multiply the exponent part by 10 (which means add 1 to the exponent): 2.5094387 * 10^11 That's the answer. Now let's do a division problem in the same way: (4.567839 * 10^6) / (5.493711 * 10^4) (4.567839 / 5.493711) * (10^6 / 10^4) (4.567839 / 5.493711) * 10^(6-4) 0.831467 * 10^2 Again we need to get the numeric part into the right range. This time it's too small, so we multiply the numeric part by 10 and divide the exponent part by 10 (that is, subtract 1 from the exponent): 8.31467 * 10^1 Are you ready for addition? I'll use the same two numbers: (4.567839 * 10^6) + (5.493711 * 10^4) In order to add two numbers in scientific notation, you must first make the exponent parts the same. Rewrite the number with the smaller exponent. In this case, we want to make the second number have an exponent of 6, which means we must multiply the exponent part by 100 (add 2 to the exponent). We divide the numeric part by 100 (move the decimal point two places left) to keep the number the same. (4.567839 * 10^6) + (0.05493711 * 10^6) Now we can use the distributive property to combine the exponents: (4.567839 + 0.05493711) * 10^6 Do the addition. 4.622776 * 10^6 That's the answer. Because I kept the higher of the two exponents, the numeric part is likely to be in the right range (1 to 10), as it is here. If it isn't, make the same kind of adjustment that I showed above. I hope this summary helps you. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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