scientific notation

Question

the mass of the moon is about 7.3x10^22kg. It would take approximately 26000000 moons to equal the mass of the sun. what is the mass of the sun

Answer 1

The problem states, in other words, that the mass of the sun is about 26 million times larger than the mass of the moon.  Therefore, if we know what the mass of the moon is, we just need to multiply it by 26 million and that will give us the mass of the sun:

 

Mass of the sun = Mass of the moon x 26 million

 

Mass of the sun = (7.3 x 10²²)(26000000) 

Now, let's write 26000000 in scientific notation.  That is: 2.6 x 10⁷

 

Mass of the sun = (7.3 x 10²²)(2.6 x 10⁷)

 

Mass of the sun = 18.98 x 10²⁹ or:  1.898 x 10³⁰

 

Answer:  The mass of the sun is approximately 1.898 x 10³⁰ Kgs.

 

 

Answer 2

Hello Jojo,

 

This is a basic multiplication problem.  But first convert 26000000 moons to the form 2.6 x 10^7 moons.  This is done by counting the digits to the left of the decimal point.  This puts the moon number in scientific notation.  

 

Next, multiply 2.6 X 7.3 = 18.98 and then add the exponents of 10^22 and 10^7 which equals 10^29.  To this point your answer would be 18.98 x 10^29.  

 

To complete the problem, 18.98 is changed to 1.9 x 10. This because all the numbers that the problem is dealing with have only one digit to the right of the decimal point.  The exponent of the 10, which is 1, is added to the exponent of the 10^29 to become 10^30 and therefore the final answer is 1.9 x 10^30 kg. 

 

I hope this helps.  If you would like additional tutoring please contact me.

 

All the best,

 

Thomas