Question

How many times is 4 × 104 larger than 2 × 102 ?(1 point)

200

2,000

20

2

Answer 1

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

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

This can be simplified step by step:

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

2. Divide the powers of 10:
\[
\frac{10^4}{10^2} = 10^{4-2} = 10^2
\]

Now, combine the results:
\[
2 \times 10^2
\]

Since \( 10^2 = 100 \):
\[
2 \times 100 = 200
\]

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

The answer is \( 200 \).