What is the digit in the thousandths place of the decimal equivalent of $\frac{3}{16}$?
Since the denominator of $\dfrac{3}{16}$ is $2^4$, we multiply numerator and denominator by $5^4$ to obtain  \[
\frac{3}{16} = \frac{3\cdot 5^4}{2^4\cdot 5^4} = \frac{3\cdot 625}{10^4} = \frac{1875}{10^4} = 0.1875.
\] The digit in the thousandths place is $\boxed{7}$.
7
Level 2
Number Theory
Problem: What is the digit in the thousandths place of the decimal equivalent of $\frac{3}{16}$?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the digit in the thousandths place of the decimal equivalent of $\frac{3}{16}$, first, convert the fraction to a decimal. This can be done by performing the division of 3 by 16. 

Start with the long division of 3.000 by 16. 

1. 16 goes into 30 once, giving 1. Multiply 1 by 16 to get 16. Subtract 16 from 30 to get 14.
2. Bring down the next 0, making it 140. 16 goes into 140 eight times, giving 8. Multiply 8 by 16 to get 128. Subtract 128 from 140 to get 12.
3. Bring down the next 0, making it 120. 16 goes into 120 seven times, giving 7. Multiply 7 by 16 to get 112. Subtract 112 from 120 to get 8.
4. Bring down the next 0, making it 80. 16 goes into 80 five times, giving 5. Multiply 5 by 16 to get 80. Subtract 80 from 80 to get 0.

The division results in 0.1875. 

Next, identify the thousandths place in the decimal 0.1875. The digits in the decimal are as follows: 
- The first digit after the decimal point (tenths) is 1.
- The second digit (hundredths) is 8.
- The third digit (thousandths) is 7.

Thus, the digit in the thousandths place is 7.<|END_OF_LATENT|> The final answer is $7$.