Question

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

Answer 1

To find how many times \( 4 \times 10^4 \) is larger than \( 2 \times 10^2 \), you can divide the first expression by the second:

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

First, simplify the fraction:

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

Calculating \( \frac{4}{2} \):

\[
= 2
\]

Now calculate \( \frac{10^4}{10^2} \):

Using the property of exponents \( \frac{a^m}{a^n} = a^{m-n} \):

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

Putting it all together:

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

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

Thus, the answer is **200**.