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How to simplify and write in scientific notation rounded to 2 digits: 3.5 x 10^2/8.9 x...

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aziaslam | Student, Undergraduate | (Level 1) Honors

Posted April 23, 2012 at 4:30 PM via web

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How to simplify and write in scientific notation rounded to 2 digits:

3.5 x 10^2/8.9 x 10^-3

 

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted April 23, 2012 at 4:43 PM (Answer #1)

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You need to remember that a negative power means the reverse of this power such that:

`10^(-3) = 1/(10^3)`

`(3.5*10^2)/(8.9*10^(-3)) = (3.5*10^2)/(8.9*(1/(10^3)))`

`(3.5*10^2)/(8.9*10^(-3)) = (3.5*10^2*10^3)/(8.9)`

You need to add the exponents of the base 10 such that:

`10^2*10^3 = 10^(2+3) = 10^5`

`(3.5*10^2)/(8.9*10^(-3)) = (3.5*10^5)/8.9`

`(3.5*10^2)/(8.9*10^(-3)) =350000/8.9`

`(3.5*10^2)/(8.9*10^(-3)) = 350000/ (89/10) `

`3500000/89= 39325.84`

Hence, evaluating the result of expression yields `(3.5*10^2)/(8.9*10^(-3)) = 39325.84.`

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