Multiplying negative powers of 10 inquiry.

Question

Good afternoon. Mind blown on this one. I am a homeschooling father with an interesting problem. When multiplying negative powers of 10 the process is to simply add them together, thus (e-2)(e-4)=e-6... But on the following problem, the answer key and my calculator both reflect that (-4)+(-7)=-10 for some reason. So I could use help explaining how this is happening.

 

Why does my calculator show (2.4e-4)(5e-7) to be 1.2e-10 and not 1.2e-11?

Answer 1

Multiply the constants and add the exponents.

 

(2.4 x 5)e^{(-4 + -7)} = 12e^-11

 

e^-11 means (x 10^-11) in the calculators

 

Since a number has to be between 1 and 10 to be scientific notation,

 

12 x 10^-11 = 1.2 x 10^-10 = 1.2e^-10

 

 

When the decimal was moved to the left to make the number smaller, the exponent had to be change to keep its value equivalent.

Answer 2

(2.4 x 10^-4)(5 x 10^-7) = (2.4)(5) x 10^-4-7 = 12 x 10^-11

 

Now put it in standard notation by moving the decimal point one digit to the left and by increasing the power in the exponent by 1.

 

12 x 10^-11 = 1.2 x 10^-10