Convert the following into correct scientific notation:

Question

I got the numbers right, but not the correct powers.

a) 445.5 X 10⁴ I got 4.455 X 10 to the? It is not power 4 and it is not power 2

b) 7804.7 X 10^-6 I got 7.8047 X 10 to the? It is not power -6 and it is not power 3

c) 0.013 X 10^-8 I got 1.3 X 10 to the? It is not power -8 and it is not power -2

Please explain how you get the correct power.

Answer 1

a) 445.5 X 10⁴ = 44.55x10⁵ = 4.455x10⁶ (every time you move 1 to the left, raise power by 1)

b) 7804.7 X 10^-6 = 780.47x10^-5 = 780.47x10^-4 = 78.047x10^-3 = 7.8047x10^-2 (every time you move 1 to the left, reduce power by1)

c) 0.013 X 10^-8 = 0.13x10^-9 = 1.3x10^-10 (every time you move 1 to the left, increase the power by -1)

Answer 2

For a, you need to move two decimal places to the left, so the power will increase by two,

also, correct notation normally has only 3 sig figs, so the answer should be 4.56 x10^6

For b, you are moving to the left 3 spaces, so add 3, giving you 7.80x10-3

For c, you need to move two spaces to the right now, so you subtract from the power,

which would mean you subtract by 2, giving you 2.3 x 10^-10