Simplifying calculations

SIMPLIFYING calculations can be done when the same number appears on the top and the bottom of the calculation. The numbers that appear on top and bottom cancel each other.

Example:

You can spend all day solving this, or plug it all into your calculator and hope you didn't hit any wrong buttons -- or you can simplify it.

First, cancel out any identical numbers on top and bottom

Then deal with the scientific notation. You know that 10¹² X 10^-2 = 10 ^{(12 + -2)} = 10¹⁰
And you know that 10¹⁰/10⁸ is 10 ^(10-8) = 10². So you can cross out all the powers of ten and replace them with a single 10².

Now, are there any common factors you can take out of the top and bottom? For instance, are there any numbers you can divide by 4? By 2?

This equation has now been simplified to:

And you can estimate the answer.

Simplify the following equations and estimate their answers: