Why might you use a different power of 10 instead of leaving both
numbers in scientific notation?
Because scintific notation is a simplification for large or small numbers, so a big number with a lot of zeros can be writen by a power of 10 multiplied by a number. But we cannot make substractions using this, because the powers ten represents very different values, for instance
[tex]\begin{gathered} 1\times10^1=10 \\ 1\times10^2=100 \end{gathered}[/tex][tex]1\times10^2-1\times10^1=100-10=90,[/tex]
But if they have the same power, we can use the distibutive law to make the substraction
[tex]1\times10^2-1\times10^1=10\times10^1-1\times10^1=(10-1)\times10^1=9\times10^1^{}[/tex]
which is the same thing. No matter the power of 10, if the power is the same you can use the same argument I've made before.
