Question

How do you simplify `\frac { 7\times 10^ { 12} } { 14,000,000,000,000}`?

Answer 1

`1/2`

Explanation:

`=(7cancel(,000,000,000000))/(14cancel(,000,000,000000)=7/14=1/2`

Alternatively,
`=(7*cancel(10^12))/(14*cancel(10^12))=1/2`

Answer 2

`1/2` or `0.5`

Explanation:

The first thing we should do is have both numerator and denominator "look" the same. To do that we either expand the numerator by writing however many zeroes are represented by the exponent of the 10 after the number (in this case 12 zeroes) OR rewrite the denominator in scientific notation, by counting the zeroes after the number and making that number an exponent of 10 (in this case there are 12 zeroes after the 14). That will either look like this:

`(7,000,000,000,000)/(14,000,000,000,000)`

OR it will look like this:

`(7xx10^12)/(14xx10^12)`

In the first case we can see 12 zeroes on both top and bottom that we can cross out, or, in the second case, we see `10^12` in both that we can cross out. Either way we end up with:

`7/14`

Finally we can divide both numbers by 7 so that we get:
`cancel 7^1/cancel14^2=1/2` or `0.5`