Question

Express your answer in scientific notation.
\[6.4 \cdot 10^5 + 36{,}000 = \]

Answer 1

To express the sum \(6.4 \cdot 10^5 + 36{,}000\) in scientific notation, we first need to convert \(36{,}000\) into scientific notation.

The number \(36{,}000\) can be rewritten as:
\[
36{,}000 = 3.6 \cdot 10^4
\]

Now, we have:
\[
6.4 \cdot 10^5 + 3.6 \cdot 10^4
\]

To add these two numbers, we need to express them with the same exponent. We will convert \(3.6 \cdot 10^4\) to have the same exponent as \(6.4 \cdot 10^5\). This involves raising the exponent from \(10^4\) to \(10^5\):

\[
3.6 \cdot 10^4 = 3.6 \cdot 10^4 \cdot \frac{10^1}{10^1} = 3.6 \cdot 10^5 \cdot 0.1 = 0.36 \cdot 10^5
\]

Now, we can add the two terms together:
\[
6.4 \cdot 10^5 + 0.36 \cdot 10^5 = (6.4 + 0.36) \cdot 10^5 = 6.76 \cdot 10^5
\]

The final answer is:
\[
\boxed{6.76 \cdot 10^5}
\]