Two consecutive positive integers are multiplied. The product when rounded to the nearest hundred is 202100. Find the sum of the two positive integers.

1. Translate the rounding statement into a possible range for the product.

Since the product rounds to $202100$ to the nearest hundred,
$202050 \leq n(n+1) < 202150.$

2. Find the consecutive integers whose product lies in the range.

Test consecutive integers near $\sqrt{202100}$.

$449 \times 450 = 202050$

This lies in the range, so the integers are $449$ and $450$.

Their sum is
$449+450=899.$