We know that $10^a < 28471 < 10^b$.
Taking the logarithm base 10 of both sides, we have $a < \log_{10}{28471} < b$.
Since $a$ and $b$ are consecutive integers, the only possibility is $a = \lfloor \log_{10}{28471} \rfloor$ and $b = \lceil \log_{10}{28471} \rceil$.
Using a calculator, we find that $\log_{10}{28471} \approx 4.454$.
Therefore, $a = 4$ and $b = 5$, so $a+b = \boxed{9}$.
The answer is: 9
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The value of $\log_{10}{28471}$ is between the consecutive integers $a$ and $b$.  Find $a+b$.

### Answer:
