(4.5 x 1011)(3.1 x 104)
Our goal is to simplify this problem into scientific notation. When multiplying with exponents, we must multiply the numbers 4.5 and 3.1 first. Then add the exponents for the rest, like this...
4.5 times 3.1 = 13.95
10^11+4 = 10^15
Our new answer is... 13.95 x 10^15
Is this right? No, not yet. The answer is still not in scientific notation because 13.95 does not fall between 1 and ten.
In order to make it a number between 1 and ten, move the decimal once to the left and your new answer is 1.395 x 10^16
(10^16 because the decimal was moved another tens place)
Our answer is now in scientific notation.
4.5 times 3.1 = 13.95
10^11+4 = 10^15
Our new answer is... 13.95 x 10^15
Is this right? No, not yet. The answer is still not in scientific notation because 13.95 does not fall between 1 and ten.
In order to make it a number between 1 and ten, move the decimal once to the left and your new answer is 1.395 x 10^16
(10^16 because the decimal was moved another tens place)
Our answer is now in scientific notation.
Nicely done Alison.
ReplyDeleteOne small thing you could possibly improve - where you say "move the decimal once to the left" . . . and then change the power to 10^16, you could perhaps be a little more specific on how that happens (remember, assume your reader is another student that doesn't know much about this).