Question

How many times is 4 × 10 integer 4 larger than 2 × 10 integer2?

Answer 1

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

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

First, we can simplify this expression. Start by dividing the coefficients:

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

Next, we can simplify the powers of \( 10 \):

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

Putting it all together, we have:

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

Now, \( 10^2 \) is equal to 100, so:

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

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

The final answer is:

\[
\boxed{200}
\]

Answer 2

u sure

Answer 3

Let’s recheck the calculations step by step to ensure accuracy.

We want to find how many times \(4 \times 10^4\) is larger than \(2 \times 10^2\). This is done by calculating the ratio:

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

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

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

Now we combine these results:

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

3. **Now calculate \(2 \times 10^2\)**:
\[
2 \times 10^2 = 2 \times 100 = 200
\]

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

So the final answer is confirmed as:

\[
\boxed{200}
\]