Simplify this expression and put your answer in Scientific Notation:

Question

(5×10
6
)×(2×10
−2
) (4 points)

Step 1: the coefficients

Step 2: the exponents to simplify.

Step 3: to change the exponent for Scientific Notation

Step 4: is the final answer.

Answer 1

To simplify the expression \((5 \times 10^6) \times (2 \times 10^{-2})\) and put it in scientific notation, we will follow the steps you've outlined:

Step 1: Simplify the Coefficients

Multiply the coefficients:

\[ 5 \times 2 = 10 \]

Step 2: Simplify the Exponents

Add the exponents of 10:

\[ 10^6 \times 10^{-2} = 10^{6 + (-2)} = 10^{6 - 2} = 10^4 \]

Step 3: Combine the Results

Combine the results from Steps 1 and 2:

\[ 10 \times 10^4 \]

This can be expressed as:

\[ 10^1 \times 10^4 \]

Step 4: Change to Scientific Notation

Now add the exponents:

\[ 10^{1 + 4} = 10^5 \]

In scientific notation, \(10\) is actually \(1.0 \times 10^1\), therefore:

\[ 1.0 \times 10^1 \times 10^4 = 1.0 \times 10^{5} \]

Final Answer

Thus, the final answer in scientific notation is:

\[ \boxed{1.0 \times 10^5} \]