The problem asks us to identify the true statements from a list of comparisons involving numbers in scientific notation. We need to determine if the given multiplicative relationship between the two numbers in each statement holds true.

1. Problem Description

The problem asks us to identify the true statements from a list of comparisons involving numbers in scientific notation. We need to determine if the given multiplicative relationship between the two numbers in each statement holds true.

2. Solution Steps

* Statement 1: $5 \times 10^{-1}$ is 0.1 times as much as $5 \times 10^{-2}$.

This means we need to check if $5 \times 10^{-1} = 0.1 \times (5 \times 10^{-2})$.

$0.1 \times (5 \times 10^{-2}) = 10^{-1} \times (5 \times 10^{-2}) = 5 \times 10^{-1-2} = 5 \times 10^{-3}$.

Since $5 \times 10^{-1} \neq 5 \times 10^{-3}$, this statement is false.

* Statement 2: $9 \times 10^{-4}$ is 1.5 times as much as $6 \times 10^{-4}$.

This means we need to check if $9 \times 10^{-4} = 1.5 \times (6 \times 10^{-4})$.

$1.5 \times (6 \times 10^{-4}) = (1.5 \times 6) \times 10^{-4} = 9 \times 10^{-4}$.

Since $9 \times 10^{-4} = 9 \times 10^{-4}$, this statement is true.

* Statement 3: $2 \times 10^{-7}$ is 0.05 times as much as $4 \times 10^{-6}$.

This means we need to check if $2 \times 10^{-7} = 0.05 \times (4 \times 10^{-6})$.

$0.05 \times (4 \times 10^{-6}) = 0.05 \times 4 \times 10^{-6} = 0.2 \times 10^{-6} = 2 \times 10^{-1} \times 10^{-6} = 2 \times 10^{-7}$.

Since $2 \times 10^{-7} = 2 \times 10^{-7}$, this statement is true.

* Statement 4: $6 \times 10^{6}$ is 20 times as much as $3 \times 10^{4}$.

This means we need to check if $6 \times 10^{6} = 20 \times (3 \times 10^{4})$.

$20 \times (3 \times 10^{4}) = 20 \times 3 \times 10^{4} = 60 \times 10^{4} = 6 \times 10^{1} \times 10^{4} = 6 \times 10^{5}$.

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

3. Final Answer

The true statements are:

$9 \times 10^{-4}$ is 1.5 times as much as $6 \times 10^{-4}$.

$2 \times 10^{-7}$ is 0.05 times as much as $4 \times 10^{-6}$.