Determine Place Values in 0.364: Decimal Position Analysis

To tackle this problem, we need to focus on the concept of decimal place values and how they translate into verbal expressions. Let's detail the steps involved:

• Step 1: Identify the given number.
  The decimal number provided is $0.364$.
• Step 2: Understand the place value of each digit.
  - The digit $3$ is in the tenths position.
  - The digit $6$ is in the hundredths position.
  - The digit $4$ is in the thousandths position.
• Step 3: Convert the decimal number into a verbal expression.
  Given the position of the digits, $0.364$ can be represented as three hundred and sixty-four thousandths, which accurately expresses the entire number in terms of its decimal place values.

After taking these steps, we conclude that the decimal 0.364 in words should be represented as "three hundred and sixty-four thousandths."

Therefore, the correct answer to this problem is three hundred and sixty-four thousandths.