Decimal Place Value: Finding 3 in Tenths and 9 in Thousandths Positions

To solve this problem, we'll follow these steps:

• Step 1: Analyze the tenths digit of each number.
• Step 2: Examine the thousandths digit of each number.
• Step 3: Confirm which number meets both digit conditions.

Now, let's work through each step:
Step 1: For number $943.578$, the tenths digit is '5'.
Step 1: For number $943.309$, the tenths digit is '3'.
Step 1: For number $578.308$, the tenths digit is '3'.
Step 1: For number $578,409$, the tenths digit is incorrectly formatted for analysis as a decimal.

Step 2: For number $943.578$, the thousandths digit is '8'.
Step 2: For number $943.309$, the thousandths digit is '9'.
Step 2: For number $578.308$, the thousandths digit is '8'.

Step 3: Examining conditions, $943.309$ has '3' as the tenths digit and '9' as the thousandths digit. The number $943.309$ perfectly matches the specified conditions.

Therefore, the solution to the problem is 943.309.