Question

adding numbers in scientific notation example

Answer 1

Adding numbers in scientific notation involves a few simple steps. Here’s a step-by-step example to illustrate the process.

### Example:

Suppose we want to add the following two numbers in scientific notation:

1. \( 3.5 \times 10^4 \)
2. \( 2.1 \times 10^5 \)

### Step 1: Ensure the Exponents are the Same

Since the exponents are different (\(10^4\) and \(10^5\)), we need to convert them to have the same exponent. It’s usually easiest to convert the smaller exponent to match the larger one.

Convert \(3.5 \times 10^4\) to an equivalent number with an exponent of \(10^5\):

\[
3.5 \times 10^4 = 0.35 \times 10^5
\]

### Step 2: Add the Numbers

Now that both numbers have the same exponent, we can add them:

\[
0.35 \times 10^5 + 2.1 \times 10^5 = (0.35 + 2.1) \times 10^5
\]

Now add the coefficients:

\[
0.35 + 2.1 = 2.45
\]

So now we have:

\[
2.45 \times 10^5
\]

### Final Result

The sum of \(3.5 \times 10^4\) and \(2.1 \times 10^5\) in scientific notation is:

\[
2.45 \times 10^5
\]

This is the final answer.