Question

Check my work please
4.5×10^3/9×10^7
4.5/9×(10^3+10^7)
1×10^10
=10^10

Answer 1

Simplify the quotient write your answer in scientific notation

Answer 2

Did you start with
\[4.5 \times 10^3 \over 9 \times 10^7\]

Answer 3

Yea

Answer 4

Think?

Answer 5

Oh know?

Answer 6

Alright well to start, the number in the numerator is smaller than the number in the denominator. This means you already know the answer is going to be less than 1 before you even do anything - meaning it can't be 10^10!

Let's start by separating the numbers to make things easier to handle:

\[{4.5 \over 9} \times {10^3 \over 10^7}\]
Can you simplify either of those fractions?

Answer 7

1 × 2^3/2^7

Answer 8

Or 1/1^3/1^7?????

Answer 9

4.5/9×10^3/10^7. = 1/2×1/10^4. = 1/2×10^4.

Answer 10

Ok let's back up a bit. 4.5 is a harder number to work with, so let's multiply it by 2 to get 9. But if we multiply the numerator by 2, we need to do the same to the denominator - so the 9 becomes an 18:

\[{9 \over 18} \times {10^3 \over 10^7}\]
That first fraction simplifies to ½!

\[{1 \over 2} \times {10^3 \over 10^7}\]
Which is the same as saying:

\[0.5 \times {10^3 \over 10^7}\]
Now for the second fraction. Whenever you're dividing exponents, if the numbers have the same base (in this case 10), you keep the base and subtract the exponents. Here we have 10^3 / 10^7. Same base, so we can subtract the exponents to get 10^(3-7) = 10^(-4). SO now we have:

\[0.5 \times 10^{-4}\]
Now we're almost done. For scientific notation, you can't have a number that begins with 0, so we need to do something about that 0.5. Luckily for us, 0.5 is just 5 that has been divided by 10, or 5 times 10^(-1):

\[5 \times 10^{-1} \times 10^{-4}\]
Now one last simplifying step: we can combine those two 10's with another exponent rule. When multiplying exponents with like bases, you keep the base and add the exponents. So 10^(-1) x 10^(-4) becomes 10^[(-1)+(-4) = 10^(-5). This leaves us with our final answer, which is:

\[5 \times 10^{-5}\]
Does that makes sense? I tried to do it step by step so you'd understand. If you have any questions please let me know!

Answer 11

That makes sense. Thank u so much

Answer 12

No problem!