Question 534183
As calculations with scientific notations go, this is an easy one. (I am including a more complicated example below).
{{{(5.2 * 10^7) / (3.15 * 10^3)=(5.2 / 3.15 )( 10^7 / 10^3)=1.651* 10^(7-4)=1.651* 10^3}}}
However, a scientist would not report a result with that many decimal places. It would be too many significant figures, because the factor
{{{5.2 * 10^7}}}
is given with only two digits, which usually means that it comes from a measurement that is not precise and accurate enough to be certain of one more digit.
EXAMPLE OF WHEN SCIENTIFIC NOTATION GETS A BIT MORE COMPLICATED:
If it was {{{(2.76 * 10^7) / (3.15 * 10^3)}}}, a simple calculation, like the one above would give you a results that is not in scientific notation:
{{{(2.76 * 10^7) / (3.15 * 10^3)=(2.76 / 3.15 )( 10^7 / 10^3)=0.876*10^3}}}
Scientific notation requires the number multiplied by the power of 10 to be 1 or more, but less than 10.
{{{0.876*10^3}}} does not qualify, but {{{0.876=8.76*(1/10)=8.76*10^-1}}},
so you do one more calculations to get to scientific notation
{{{0.876*10^3=(8.76*10^-1)*10^3=8.76*10^2}}}
{{{8.76*10^2}}} is in scientific notation.