Question
How many times is 4 × 104 larger than 2 × 102?(1 point)
Responses
2,000
2,000
20
20
200
200
2How many times is 4 × 104 larger than 2 × 102?(1 point)
Responses
2,000
2,000
20
20
200
200
2
Responses
2,000
2,000
20
20
200
200
2How many times is 4 × 104 larger than 2 × 102?(1 point)
Responses
2,000
2,000
20
20
200
200
2
Answers
GPT-4o mini
To determine how many times \( 4 \times 10^4 \) is larger than \( 2 \times 10^2 \), we can first calculate the values of each expression:
1. Calculate \( 4 \times 10^4 \):
\[
4 \times 10^4 = 4 \times 10000 = 40000
\]
2. Calculate \( 2 \times 10^2 \):
\[
2 \times 10^2 = 2 \times 100 = 200
\]
Next, we divide the first result by the second to find how many times larger it is:
\[
\frac{40000}{200} = 200
\]
Thus, \( 4 \times 10^4 \) is **200 times** larger than \( 2 \times 10^2 \).
The correct response is:
**200**
1. Calculate \( 4 \times 10^4 \):
\[
4 \times 10^4 = 4 \times 10000 = 40000
\]
2. Calculate \( 2 \times 10^2 \):
\[
2 \times 10^2 = 2 \times 100 = 200
\]
Next, we divide the first result by the second to find how many times larger it is:
\[
\frac{40000}{200} = 200
\]
Thus, \( 4 \times 10^4 \) is **200 times** larger than \( 2 \times 10^2 \).
The correct response is:
**200**