Question

Perform the following operation
and express the answer in
scientific notation.
7.30x102 + 2.80x103

Answer 1

To do the sum of two numbers in scientific notation we must put them in the same exponent, therefore, if we want to sum

$7.30\times10^2+2.80\times10^3$

We must put both coefficients in 2 or 3, we can choose, I'll put the 2.8 in exponent 2, therefore

$7.30\times10^2+28.0\times10^2$

Now we can preserve the exponent and sum the coefficient

$\begin{gathered} 7.30\times10^2+28.0\times10^2=(28.0+7.3)\times10^2 \\ \\ (28.0+7.3)\times10^2=35.3\times10^2 \end{gathered}$

Therefore we have

$7.30\times10^2+2.80\times10^3=35.3\times10^2$

But see that the result is not in scientific notation, so let's adjust it:

$35.3\times10^2=3.53\times10^3$

Therefore, the result in scientific notation is

$7.30\times10^2+2.80\times10^3=3.53\times10^3$

The coefficient (green) is 3.53 and the exponent (yellow) is 3