# How do you divide #(3.0 x 10^4)/ (7 x 10^-7) #?

##### 1 Answer

I believe the question is about simplifying the number written as

(it's a sign of multiplication, not a variable

The answer is (approximately)

It is an approximate value because a *rational number* *decimal fraction*, it's "precise" value is a *periodical* decimal fraction with *period*. So, the precise decimal representation of the original number is *period*.

Now about why the answer is as specified above.

It's all about *exponents*. Negative exponent is used as a replacement for *multiplicative inverse* numbers (*multiplicative inverse* of

Thus,

It's not just a syntactical convenience, there is a very good mathematical reason for this representation based on the rules of multiplication of numbers expressed as exponents with the same base:

You can learn the details of how to deal with exponential functions at Unizor by following the menu items *Algebra* and *Exponential Functions*.

Using the above mention rule about negative exponents, you can replace

which, in turn, using the rule of multiplication of exponential numbers with the same base

All we have to do next is to represent

where the parenthesis are used to specify a *periodical* decimal fraction.