How many times is 4 × 10^4 larger than 2 × 10^2

Question

Responses:

20
20

200
200

2
2

2,000
2,000

Answer 1

To determine how many times \(4 \times 10^4\) is larger than \(2 \times 10^2\), we can divide the two values:

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

First, simplify the expression:

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

Calculating each part:

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

Now, combine the results:

\[ 2 \times 10^2 = 2 \times 100 = 200 \]

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

So the correct response is:

200