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Mathematics
OpenStudy (anonymous):

this is the third time iam asking..please help!! Write in Scientific and Decimal Notation (3.16x10^3)(24x10^2)

OpenStudy (anonymous):

7.58X10^6

OpenStudy (anonymous):

can u explain how to do it? i have a final coming up and i needa know all of this

OpenStudy (anonymous):

significant figuresdasdaerasdsfda

OpenStudy (mertsj):

For a number to be in scientific notation, it has to have two factors. The first factor must be between 1 and 10 and the second factor must be a power of 10.

OpenStudy (anonymous):

i still dont understand

OpenStudy (mertsj):

So when you multiply those two numbers you get 75.84 x 10^5

OpenStudy (anonymous):

ohhhhh...so thts the answer in scientific notation! then whadda bout decimal?

OpenStudy (mertsj):

That is not scientific notation because 75.84 is not between 1 and 10.

OpenStudy (anonymous):

oh...umm..

OpenStudy (mertsj):

To make it between 1 and 10 we have to move the decimal point 1 place to the left making it 7.584

OpenStudy (anonymous):

First you have to consider the number of significant digits, you go by the term with the lowest amount of significance (24x10^2 in this case has 2 significant digits). Then its a simple matter of multiplication... To convert from scientific notation to decimal notation, you move the decimal place by the amount indicated on the power. (ie, 1x10^2 becomes 100) To go from decimal notation to scientific notation you figure out how many times you must multiply by 10 to reach a point where the number before the decimal is between 1 and 10.

OpenStudy (anonymous):

\[(3.16\times 10^3)(24\times 10^2)=3.16\times 24\times 10^{3+2}\] \[=75.84\times 10^5=75.85\times 100000=7585000=7.54\times 10^6\]\]

OpenStudy (mertsj):

However we have no right to change the answer so we have to fix what we just did and the way to fix it is to make the exponent 1 greater

OpenStudy (mertsj):

So now the second factor is 10^6 and our final answer is 7.584 x 10^6

OpenStudy (anonymous):

ohh...okay :D thanks everybody

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