We are asked to select all the true statements from the following: 1. $4 \times 10^{-7}$ is 0.2 times as much as $2 \times 10^{-5}$.

1. Problem Description

We are asked to select all the true statements from the following:

1. $4 \times 10^{-7}$ is 0.2 times as much as $2 \times 10^{-5}$.

2. $2 \times 10^5$ is 40 times as much as $5 \times 10^4$.

3. $6 \times 10^4$ is 2 times as much as $3 \times 10^4$.

4. $7 \times 10^{-5}$ is 0.1 times as much as $7 \times 10^{-3}$.

2. Solution Steps

Statement 1: $4 \times 10^{-7}$ is 0.2 times as much as $2 \times 10^{-5}$.

We need to check if $4 \times 10^{-7} = 0.2 \times (2 \times 10^{-5})$.

$0.2 \times (2 \times 10^{-5}) = 0.4 \times 10^{-5} = 4 \times 10^{-1} \times 10^{-5} = 4 \times 10^{-6}$.

Since $4 \times 10^{-7} \neq 4 \times 10^{-6}$, this statement is false.

Statement 2: $2 \times 10^5$ is 40 times as much as $5 \times 10^4$.

We need to check if $2 \times 10^5 = 40 \times (5 \times 10^4)$.

$40 \times (5 \times 10^4) = 200 \times 10^4 = 2 \times 10^2 \times 10^4 = 2 \times 10^6$.

Since $2 \times 10^5 \neq 2 \times 10^6$, this statement is false.

Statement 3: $6 \times 10^4$ is 2 times as much as $3 \times 10^4$.

We need to check if $6 \times 10^4 = 2 \times (3 \times 10^4)$.

$2 \times (3 \times 10^4) = 6 \times 10^4$.

Since $6 \times 10^4 = 6 \times 10^4$, this statement is true.

Statement 4: $7 \times 10^{-5}$ is 0.1 times as much as $7 \times 10^{-3}$.

We need to check if $7 \times 10^{-5} = 0.1 \times (7 \times 10^{-3})$.

$0.1 \times (7 \times 10^{-3}) = 0.7 \times 10^{-3} = 7 \times 10^{-1} \times 10^{-3} = 7 \times 10^{-4}$.

Since $7 \times 10^{-5} \neq 7 \times 10^{-4}$, this statement is false.

However, we need to reread the question, since all the check marks are selected, maybe the image is misleading.

Statement 1: $4 \times 10^{-7}$ is 0.2 times as much as $2 \times 10^{-5}$.

$0.2 \times (2 \times 10^{-5}) = 0.4 \times 10^{-5} = 4 \times 10^{-1} \times 10^{-5} = 4 \times 10^{-6}$.

Then $4 \times 10^{-7}$ is 0.1 times as much as $4 \times 10^{-6}$

Statement says it's 0.2 times as much as $2 \times 10^{-5}$, so false.

Statement 2: $2 \times 10^5$ is 40 times as much as $5 \times 10^4$.

$40 \times (5 \times 10^4) = 200 \times 10^4 = 2 \times 10^2 \times 10^4 = 2 \times 10^6$.

Statement says $2 \times 10^5$ is 40 times as much as $5 \times 10^4$ so false.

Statement 3: $6 \times 10^4$ is 2 times as much as $3 \times 10^4$.

$2 \times (3 \times 10^4) = 6 \times 10^4$. Statement says $6 \times 10^4$ is 2 times as much as $3 \times 10^4$ so true.

Statement 4: $7 \times 10^{-5}$ is 0.1 times as much as $7 \times 10^{-3}$.

$0.1 \times (7 \times 10^{-3}) = 0.7 \times 10^{-3} = 7 \times 10^{-1} \times 10^{-3} = 7 \times 10^{-4}$.

Statement says $7 \times 10^{-5}$ is 0.1 times as much as $7 \times 10^{-3}$, so false.

After rereading it, statement 2 is true. $2 \times 10^5$ is 4 times $5 \times 10^4$. No, that's wrong.

$2 \times 10^5 = 200000$

$5 \times 10^4 = 50000$

$200000 / 50000 = 4$

So statement 2 says that $2 \times 10^5$ is 40 times as much as $5 \times 10^4$. This is wrong, it should be 4 times. So it's false.

3. Final Answer

$6 \times 10^4$ is 2 times as much as $3 \times 10^4$.