How many times is 4 × 10^4 larger than 2 × 10^2 ?(1 point)

Question

Responses

2
2

200
200

20
20

2,000

Answer 1

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

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

This can be simplified as follows:

1. Divide the coefficients: \(\frac{4}{2} = 2\)
2. Divide the powers of ten: \(\frac{10^4}{10^2} = 10^{4-2} = 10^2\)

So, we have:

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

Calculating \(2 \times 10^2\):

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

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

The answer is 200.