How many times is 4 × 10^4

Question

larger than 2 × 10^2
?(1 point)
Responses

20
20

200
200

2,000
2,000

2

Answer 1

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

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

First, simplify the fraction:

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

Calculating the first part:

\[ \frac{4}{2} = 2 \]

Now calculate the second part using the property of exponents:

\[ \frac{10^4}{10^2} = 10^{4-2} = 10^2 = 100 \]

Now multiply these results together:

\[ 2 \times 100 = 200 \]

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

The correct response is:

200