1. **Stating the problem:** Determine the place value to the thousandths of a digit in a given decimal number. 2. **Understanding place values:** In a decimal number, the place values to the right of the decimal point are tenths, hundredths, thousandths, and so on. 3. **Place value positions:** - The first digit to the right of the decimal point is the tenths place. - The second digit is the hundredths place. - The third digit is the thousandths place. 4. **Example:** Consider the decimal number $12.3456$. - The digit in the thousandths place is $5$. - Its place value is $5 \times \frac{1}{1000} = \frac{5}{1000} = 0.005$. 5. **General formula:** For a digit $d$ in the thousandths place, its place value is: $$ \text{Place value} = d \times \frac{1}{1000} $$ 6. **Summary:** To determine the place value to the thousandths of a digit in a decimal number, identify the third digit to the right of the decimal point and multiply it by $\frac{1}{1000}$. This completes the objective.