I'm not sure how to do this question

"You are flying in an airplane on vacation. You have been told that there are less molecules in a cubic meter of air the higher in altitude you go.
a. There are 10^25 molecules in a cubic meter of air at sea level and 10^23 molecules at an altitude of 33 km. How many more molecules are there at sea level?
b. How many more molecules would there be if you went to an altitude of 50 km where there are 10^20 molecules?"

Can someone please help. thanks!

Question

I'm not sure how to do this question

"You are  flying in an airplane on vacation. You have been told that there are less molecules in a cubic meter of air the higher in altitude you go.
a. There are 10^25 molecules in a cubic meter of air at sea level and 10^23 molecules at an altitude of 33 km. How many more molecules are there at sea level?
b. How many more molecules would there be if you went to an altitude of 50 km where there are 10^20 molecules?"

Can someone please help. thanks!

mathstudent55 · Answer

The 23 and the 25 are exponents, right?

nathanielborrero321 · Answer

Yes they are

mathstudent55 · Answer

Then how about writing it as 10^25 and 10^23 so we don't have to guess?

nathanielborrero321 · Answer

Ok

mathstudent55 · Answer

At least x2 is an unusual way to write 2x, so we already think it's x^2, but 1025 is a perfectly normal looking number, so how are we supposed to know you mean 10^25 when you write 1025?

mathstudent55 · Answer

Ok, now let's look the problem since I now know how to read it.

nathanielborrero321 · Answer

Oh im sorry

mathstudent55 · Answer

a. The difference is 10^25 - 10^23 if you want subtraction.
A better way of thinking of this is to compare by division.

$\dfrac{10^{25}}{10^{23}} $

Do you know how to divide powers with the same base?

nathanielborrero321 · Answer

You subtract and put the larger the answer where the larger exponent is right?

mathstudent55 · Answer

Rule: $\dfrac{a^m}{a^n} = a^{m - n} $

When you divide powers with the same base, keep the base, and subtract the exponents.

mathstudent55 · Answer

What is 25 - 23?

nathanielborrero321 · Answer

2

mathstudent55 · Answer

Right, so the answer is $10^2$

That is equal to 10 * 10 = 100

There are 100 times more molecules of air at 33 km altitude than at sea level.

nathanielborrero321 · Answer

Thank you

mathstudent55 · Answer

Perhaps the problem really wants you to do the subtraction.
Are you learning scientific notation?

nathanielborrero321 · Answer

Yes I learned it

mathstudent55 · Answer

$10^{25} - 10^{23} =$

$=100 \times 10^{23} - 1 \times 10^{23}$

$= 99 \times 10^{23} $

$= 9.9 \times 10^{24} $

That is the actual difference after subtracting the numbers.

nathanielborrero321 · Answer

Ok thanks

mathstudent55 · Answer

You're welcome.

nathanielborrero321 · Answer

What about part b