Question

Fill in the blanks.

Simplify this expression and put your answer in Scientific Notation:
(5×10
6
)×(2×10
−2
) (4 points)

Step 1 Word Bank: (Add, Subtract, Multiply, Divide) the coefficients

Step 2 Word Bank: (Add, Subtract, Multiply, Divide) the exponents to simplify.

Step 3 Word Bank: (Add to the exponent, subtract from the exponent, or Do not change the exponent) to change the exponent for Scientific Notation

Step 4 Word Bank: (2.5 x 10^4, 7.0 x 10^4, 1 x 10^5, 10 x 10^4, or 1 x 10^3) is the final answer.

Answer 1

To simplify the expression \((5×10^6)×(2×10^{-2})\) and put the answer in Scientific Notation, let's go through the steps.

1. **Step 1:** Multiply the coefficients.
- Here the coefficients are 5 and 2. So:
\(5 × 2 = 10\)

2. **Step 2:** Add the exponents to simplify.
- The exponents are 6 and -2. So:
\(6 + (-2) = 6 - 2 = 4\)

3. **Step 3:** Change the exponent for Scientific Notation.
- The expression we have now is \(10 × 10^4\). To write this in proper Scientific Notation, we need the coefficient to be between 1 and 10.
- So we can write:
\(10 × 10^4 = 1 × 10^5\) (because \(10 = 1 × 10^1\) and \(10^1 × 10^4 = 10^{1+4} = 10^5\))

4. **Step 4:** The final answer is \(1 × 10^5\).

So, filling in the blanks:

Step 1: Multiply the coefficients
Step 2: Add the exponents to simplify
Step 3: Do not change the exponent to change the exponent for Scientific Notation
Step 4: \(1 x 10^5\) is the final answer.