could someone help me with scientific notation?

Question

(4.3×10^-3)(3×10^-4)

 

i know to multiply 3 and 4.3 but im so confused about the exponents could someone explain what i do?

 

Answer 1

When dealing with exponents there are a few things to think about.

 

You already know to multiply the 3 and 4.3 so let's focus on the 10^x.

 

In this case you have...

10^-3 * 10^-4

 

When you multiply similar numbers with an exponent you simply have to add the exponents.  (This only works if the base is the same ex. 5³*5⁶ or 11^-23*11⁸ but not in the case of 4³*7⁸ because the base is not the same)

 

(-3)+(-4)= -7

 

 

so you end up with 10^-7

 

This works because 10^-3 is the same thing as 1/10³ and 10^-4 = 1/10⁴

if you multiply...

      1                         1          

-----------    X   ----------------    

10*10*10         10*10*10*10         

 

1/10⁷ = 10^-7

 

At this point you will have 12.9 x 10^-7 but you are not done because in scientific notation there can only be one digit (and it can't be zero) to the left of the decimal.

 

The 12.9 needs to become 1.29 this can only happen if you divide 12.9 by 10 or multiply it by 10^-1.

 

Now you have 1.29 x 10^-1 x 10^-7

 

You now know that multiplying similar numbers with an exponent requires you to add the exponents.

 

(-1)+(-7)= -8

 

Therefore you final answer will read...

 

1.29 x 10^-8

 

(Keep in mind that if you had ended up with a number like 0.0129 it would need to be changed to 1.29 to fit into scientific notation.  0.0129 would need to be multiplied by 10² to get 1.29 which would have changed you 10^-7 to 10^-5.)