The number 29 is 0.8% of which number?

Introduction / Context:
This question is an example of reversing a percentage. Instead of finding a percentage of a number, we know a value and the percentage it represents of some unknown number. This is common in topics such as finance, statistics, and data interpretation, where we often know a part and its percentage share, and we must find the total.

Given Data / Assumptions:
29 is equal to 0.8 percent of some number, which we call N.
0.8 percent means 0.8 / 100 in decimal form.
We need to find the value of N such that 0.8 percent of N = 29.

Concept / Approach:
If x percent of N equals a given number V, then we can write the equation (x / 100) * N = V. To find N, we rearrange the equation as N = V * 100 / x. Here x = 0.8 and V = 29. Keep in mind that 0.8 percent is a small fraction, so the original number N must be quite large relative to 29. Substituting the values into the formula lets us quickly compute N.

Step-by-Step Solution:
Let the required number be N. We are given that 0.8 percent of N equals 29. By definition, 0.8 percent of N = (0.8 / 100) * N. So, (0.8 / 100) * N = 29. This implies N = 29 * 100 / 0.8. Compute 29 * 100 = 2900. Now divide 2900 by 0.8: 2900 / 0.8 = 3625. Therefore, 29 is 0.8 percent of 3625.

Verification / Alternative check:
To verify, calculate 0.8 percent of 3625 and confirm that the result is 29. Express 0.8 percent as 0.008. Then 0.008 * 3625 = 29. This perfect match shows that the computed value of N is correct. Any other number would not yield 29 when 0.8 percent of it is taken.

Why Other Options Are Wrong:
If N were 1450, then 0.8 percent of 1450 would be 0.008 * 1450 = 11.6, not 29. For N = 7250, 0.8 percent would be 0.008 * 7250 = 58, which is double the required value. For N = 10875, 0.8 percent would be 87, which is even larger. Only 3625 produces 29 when 0.8 percent of it is calculated.

Common Pitfalls:
One pitfall is misreading 0.8 percent as 8 percent, which would use 0.08 instead of 0.008 and lead to a much smaller N. Another common error is dividing 29 by 0.8 and forgetting to multiply by 100, or incorrectly multiplying by 0.8 instead of dividing. A careful setup of the equation (percentage / 100) * N = value, followed by correct algebraic inversion, helps avoid such mistakes.

Final Answer:
The number of which 29 is 0.8 percent is 3625.