Question

scientific operations
add these scientific notation numbers and give the answer in scientific notation:
(5 × 10²) + (2.3 × 10³)

Explanation:

Step1: Convert to same exponent

To add numbers in scientific notation, we first make the exponents of \(10\) the same. We can rewrite \(5\times10^{2}\) as \(0.5\times10^{3}\) (since \(5\times10^{2}=\frac{5}{10}\times10^{3}=0.5\times10^{3}\)) or rewrite \(2.3\times10^{3}\) as \(23\times10^{2}\). Let's use the first method: \(5\times10^{2}=0.5\times10^{3}\).

Step2: Add the coefficients

Now we have \((0.5\times10^{3})+(2.3\times10^{3})\). When the exponents of \(10\) are the same, we add the coefficients: \(0.5 + 2.3=2.8\).

Step3: Write in scientific notation

Now we combine the sum of the coefficients with the common power of \(10\). So the result is \(2.8\times10^{3}\).

Answer:

\(2.8\times10^{3}\)