The problem asks us to identify which of the given statements about scientific notation are true. We need to verify if the given multiplicative relationship between two numbers in scientific notation holds.

1. Problem Description

The problem asks us to identify which of the given statements about scientific notation are true. We need to verify if the given multiplicative relationship between two numbers in scientific notation holds.

2. Solution Steps

We need to check each statement individually.

Statement 1: $8 \times 10^{-3}$ is 200 times as much as $4 \times 10^{-5}$.

We need to check if $8 \times 10^{-3} = 200 \times (4 \times 10^{-5})$.

$200 \times (4 \times 10^{-5}) = 800 \times 10^{-5} = 8 \times 10^2 \times 10^{-5} = 8 \times 10^{-3}$.

So, the statement is TRUE.

Statement 2: $2 \times 10^6$ is 50 times as much as $4 \times 10^4$.

We need to check if $2 \times 10^6 = 50 \times (4 \times 10^4)$.

$50 \times (4 \times 10^4) = 200 \times 10^4 = 2 \times 10^2 \times 10^4 = 2 \times 10^6$.

So, the statement is TRUE.

Statement 3: $3 \times 10^{-2}$ is 0.1 times as much as $3 \times 10^{-3}$.

We need to check if $3 \times 10^{-2} = 0.1 \times (3 \times 10^{-3})$.

$0.1 \times (3 \times 10^{-3}) = 0.3 \times 10^{-3} = 3 \times 10^{-1} \times 10^{-3} = 3 \times 10^{-4}$.

Since $3 \times 10^{-2} \neq 3 \times 10^{-4}$, the statement is FALSE.

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

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

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

Since $6 \times 10^4 \neq 6 \times 10^2$, the statement is FALSE.

3. Final Answer

The true statements are:

$8 \times 10^{-3}$ is 200 times as much as $4 \times 10^{-5}$.

$2 \times 10^6$ is 50 times as much as $4 \times 10^4$.