Question

How do you simplify `(5.6498times10^10)/(8.2times10^4)`?

Answer 1

`6.9 xx 10^5`

Explanation:

When I simplify fractions, I like to keep track of the terms using parenthesis, so even though it's not the proper way to write scientific notation, I'm going to re-write the problem first.

`((5.6498)(10^10))/((8.2)(10^4))`

I like to put parenthesis around terms like this because it's easier to see where you can move things around and split the fractions. Not a big deal here, but its a handy trick for larger problems. We can see that if we split the fraction right down the middle;

`((5.6498)color(red)(|)(10^10))/((8.2)color(red)(|)(10^4))`

We can group the `10`s together and the other terms together and solve both parts separately.

`5.6498/8.2 xx 10^10/10^4`

Using long division, the fraction on the left simplifies cleanly to `.689`. To solve the fraction on the right, remember your rules for exponent division. When you divide two numbers with exponents, the exponents subtract.

`10^10/10^4 = 10^(10-4) = 10^6`

Putting both sides back together we have;

`.689 xx 10^6`

To write this properly in scientific notation, we need to move the decimal one place to the right. Remember to account for that in your exponent!

`6.89 xx 10^5`

Lastly, if you are keeping track of significant figures, your smallest term, `8.2 xx 10^4` has two, so you should round your answer to two significant figures.

`6.9 xx 10^5`