Question

One of your friends missed the class on scientific notation. Describe how you would explain to your friend what it means for a number to be in scientific notation and how to convert a number from standard form to scientific notation.

Answer 1

Scientific notation consists of a coefficient multiplied by 10 raised to an exponent . To convert to a real number, start with the base and multiply by 5 tens like this: 5.14 × 10 × 10 × 10 × 10 × 10 = 514000(here are only 4 zeros because you cancel one zero to remove decimal) so we write 5.14*10^5

to convert from 5.14*10^5 to decimal its vice versa!

Answer 2

All numbers in scientific notation have the following form:
nonzerodigit.restofnumber x 10^power

ex: 350,000,000,000,000 =3.5x10^8 because this is a whole number, and the decimal is to the far right of it. -> 350,000,000,000,000.0 <- see.
So, you move that decimal over to the right until you get to a nonzerodigit!

3.5: five would be your non0digit.
How many zero did it take you to get to it? 8

So 3.5x10^8

Ex2 .0004567
Notice that you have to move your decimal to the right to get to your non0digit?
. ->
0004.567 you moved the decimal 4 times to the right! Thus, 4.567x10^-4