# How do you write 0.07 * 10^6 in scientific notation?

Sep 15, 2015

$7 \cdot {10}^{4}$

#### Explanation:

A general form number written in exponential form

$a \cdot {10}^{b}$

must have its mantissa, which is the name given to coefficient $a$, in the interval

$1 \le | a | < 10$

Your starting number has its mantissa written as $0.07$. This means that you must use up some of those power of $10$ to get it in that interval.

So, you have

$0.07 \cdot {10}^{6} = 0.7 \cdot {10}^{5} = 7 \cdot {10}^{4}$

You now have $1 \le 7 < 10$, so this is where you stop.

Since the original number had one signifcant figure, its scientific notation version must have one significant figure as well.