Question

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

2,000
2,000

200
200

2
2

20
20
Skip to navigation

Answer 1

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

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

Now, we can simplify this step by step:

1. Divide the coefficients (4 and 2):
\[
\frac{4}{2} = 2
\]

2. Now, divide the powers of 10. Recall the property of exponents:
\[
\frac{10^4}{10^2} = 10^{4-2} = 10^2
\]

3. Now combine the results:
\[
\frac{4 \times 10^4}{2 \times 10^2} = 2 \times 10^2
\]

4. Now, we need to interpret \( 2 \times 10^2 \):
\[
2 \times 10^2 = 2 \times 100 = 200
\]

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

The correct response to your question is:
**200**.