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 200 200 20 20 2,000 2,000 2
Answers
GPT-4o mini
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**.
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**.