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

1 Answer
Jul 6, 2017

Answer:

#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#