How do you write 7,930,000,000 in scientific notation?

Feb 16, 2016

$= 7.93 \times {10}^{9}$

Explanation:

The number that has the biggest impact if it is the one that is changed. It is called $\textcolor{b l u e}{\text{ 'the most significant figure'}}$.
It is the 7 as it is counting in the biggest units.

I say the next bit the way I do to avoid some classic mistakes that occur.

Keeping the decimal place where it is, 'slid' the number 9 places to the right so that you end up with:

$7.930$ Although you have the same digits their value, written this way, has changed. So we need to convert them back to the original value.

We have reduced its value by a factor ${10}^{9}$ so we need to increase it by the same size of factor:

$7930000000 = \frac{7930000000}{\textcolor{b r o w n}{{10}^{9}}} \times \textcolor{b r o w n}{{10}^{9}}$

$= 7.93 \times {10}^{9}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In principle we have multiplied the original value by$\text{ "color(brown)( 1 )" }$but in the form of $\textcolor{b r o w n}{{10}^{9} / {10}^{9}}$