Question

How many times is 4 x 104 larger than 2 x 10²? (1 poin

O 20

O2

Ο 200

Ο 2,000

Answer 1

To find how many times \( 4 \times 10^4 \) is larger than \( 2 \times 10^2 \), we can set up the following division:

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

We can simplify this by dividing both the coefficients (the numbers in front) and the powers of ten:

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

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

Now we can combine these results:

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

Next, we compute \( 2 \times 10^2 \):

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

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

The correct answer is:

**Ο 200**