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*10^2+2.80*10^3`

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

`7.30*10^2+28.0*10^2`

Now we can preserve the exponent and sum the coefficient

`\begin{gathered} 7.30*10^2+28.0*10^2=(28.0+7.3)*10^2 \\ \\ (28.0+7.3)*10^2=35.3*10^2 \end{gathered}`

Therefore we have

`7.30*10^2+2.80*10^3=35.3*10^2`

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

`35.3*10^2=3.53*10^3`

Therefore, the result in scientific notation is

`7.30*10^2+2.80*10^3=3.53*10^3`

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