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Question 76655: Multiply. Write the answer in scientific notation.
(2.4 * 10^-5)(4 * 10^-4)
I am needing some help with this scientific notation, I am not understanding how to do this. Thanks.
Answer by wodkit02(9)   (Show Source):
You can put this solution on YOUR website! When you write a number in scientific notation, you are simply putting a single digit in front of a decimal point and multiplying the remainder of the number by some power of 10.
For example:
Express 200 in scientific notation.
I want only one number in front of the decimal point. Keep in mind that 200 is also expressed as 200.; every whole number can be expressed with a decimal point at the end of it. Thus I move the decimal point two places to the left:
200. ----- 2.00
Now to determine the power of 10 that I multiply the number by, I look at how many places I have to move the decimal point to get back to the original number. Since I have to move it two places to the RIGHT, I get:
200. ----- 2.00 X 10^2
The exponent will be positive if you move to the RIGHT and negative if you move to the LEFT. Think of a number line. Negative numbers appear on the left side, while postive numbers appear on the right side.
Now for your problem - (2.4 X 10^-5)(4 X 10^-4)
There are two ways to do this. First, we can convert each factor into its standard form (2.4 X 10^-5 = 0.000024), multiply them, and then convert the answer into scientific notation.
(2.4 X 10^-5)(4 X 10^-4) = 0.000024 X 0.0004 = 0.0000000096 = 9.6 X 10^-9
The second way is much shorter, but a little harder to recognize as correct at first. Simply multiply the first numbers of each scientific notation together (the numbers being multiplied by 10) and then add the exponents of the 10 together. If the product is not in scientific notation, convert it at the end.
(2.4 X 10^-5)(4 X 10^-4) = (2.4 X 4) X 10^(-5 + -4) = 9.6 X 10^-9
Notice how the same answer is obtained both ways.
Here is a quick example of a number that needs to be converted after the short method:
(9.89 X 10^6)(8.2 X 10^2) = (9.89 X 8.2) X 10^(6 + 2) = 81.098 X 10^8
81.098 X 10^8 = 8.1098 X 10^9
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