could someone help me with math?

Question

Simplify this expression, and enter your answer in scientific notation:

(1×10^-6)(4.5×10²⁾

——————————

2.5×10¹⁰ 

 

(btw this is supposed to be a fraction) 

Answer 1

One way to consider this type of problem is to work the initial values separately from the 10^x values.

 

1 x 4.5

----------

2.5

 

and

 

10^-6 x 10²

-----------

10¹⁰

 

Solve each and then multiply them back together.  Remember that when you multiply like numbers with exponents you simply add the exponents together and when you divide them you subtract the exponents.

 

ex. 10^-6 x 10² = 10^-4   ;      10^-4/10¹⁰ = 10^-14

 

For the answer to be in scientific notation the initial number must have only one digit to the left of the decimal.

 

Examples...

 

If you answer looks like 7.46 x 10³ it is already in scientific natation and does not need to be changed.

 

If your answer looks like this 34.78 x 10⁴  you must move the decimal to the left (in this case one spot) giving you 3.478 with this change you must also change the exponent for the ten by adding 1 to it since you moved the decimal 1 place to the left.

 

If your answer looks like this 0.056 x 10⁷ you must move the decimal to the right (in this case two spots) giving you 5.6.  With this change you must change the ten's exponent by subtracting 2 from it since you moved the decimal 2 places to the right.