An Algebra 2 math problem?

Question

This is about scientific notation and exponents.
Newton's law of gravitation can be used to compute earth's mass in grams. Applied it is 908 = 6.67 X 10^-8 x 1 x M / (6.37 x 10^8)^2. If M represents mass, what is the mass of the earth in grams?

The other one is: The mass of a proton is 1.672 x 10^-24 g. If earth's moon's mass is 7.35 x 10^22 kg, how many times larger is its mass than tha tof a proton. For this one I have 3.895.. and so on. And i rounded to 4.4 x 10^49, but I'm not sure if the answer should have to be rounded. Thanks!

Answer 1

981 = 6.67 X 10^-8 x 1 x M / (6.37 x 10^8)²
So M = 981 * (6.37 x 10^8)²/(6.67 x 10^(-8))
≈ 6.63 x 10^19 g (PS 1 newton = 981 g.m/s² not 908)

Mmoon/Mproton = 7.35 x 10^22 x 10³ g/(1.672 x 10^-24) g
≈ 4.40 x 10^49

Answer 2

I've never seen an uglier problem.

since when did they start useing numbers instead of symbols...sheesh

K, so for number one, multiply both sides by the denominator, which is (6.37 x 10^16) than divide both sides by 6.67 x 10^-8 and that number is M.

number two, yea you can round no biggie, that number is HUMONGOUS. makes a difference of like .000001%

Answer 3

First of all, gravitational acceleration is 9.80 m/s^2, but what's the problem? Did you remember to put in the units for Newton's Gravitational constant?

re your second question, you should round, but you overdid it. The second value has 3 significant digits, so you should round the answer to 3 significant digits: 4.40