Estimate Large and Small Quantities Quick Check 2 of 52 of 5 Items Question How many times is 4 × 10^4 larger than 2 × 10^2 ?(1 point) Responses 200 200 20 20 2,000 2,000 2

Answer 1

To determine how many times \(4 \times 10^4\) is larger than \(2 \times 10^2\), we can set up the following calculation:

1. Divide the two numbers:

\[ \frac{4 \times 10^4}{2 \times 10^2} \]

2. Simplify the expression:

\[ = \frac{4}{2} \times \frac{10^4}{10^2} \]

3. Calculate each part:

\[ = 2 \times 10^{4-2} \]

\[ = 2 \times 10^2 \]

4. Calculate \(10^2\):

\[ = 2 \times 100 = 200 \]

So, \(4 \times 10^4\) is 200 times larger than \(2 \times 10^2\).

The correct response is 200.