To add two numbers in scientific notation, we first need to ensure that they have the same exponent. We can choose the numbers \(3.2 \times 10^4\) and \(1.95 \times 10^6\) for this example.
Step 1: Write both numbers in standard form
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Convert \(3.2 \times 10^4\) to standard form: \[ 3.2 \times 10^4 = 32000 \]
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Convert \(1.95 \times 10^6\) to standard form: \[ 1.95 \times 10^6 = 1950000 \]
Step 2: Make the exponents the same
We need to express \(3.2 \times 10^4\) in terms of \(10^6\):
\[ 3.2 \times 10^4 = 3.2 \times 10^4 \times \frac{10^2}{10^2} = 3.2 \times 10^6 \times 10^{-2} = 0.032 \times 10^6 \]
Step 3: Add the numbers
Now we can add:
\[ 0.032 \times 10^6 + 1.95 \times 10^6 = (0.032 + 1.95) \times 10^6 = 1.982 \times 10^6 \]
Step 4: Final Result
The sum of \(3.2 \times 10^4\) and \(1.95 \times 10^6\) is:
\[ 1.982 \times 10^6 \]
This is the final answer!