1. **Problem:** Round the number 196725 to the nearest ten thousand. 2. **Formula and rule:** To round to the nearest ten thousand, look at the digit in the thousand's place (the digit immediately to the right of the ten thousand's place). 3. **Step-by-step:** - The number is 196725. - The ten thousand's place digit is 9 (in 190000). - The thousand's place digit is 6. 4. **Rounding rule:** If the digit in the thousand's place is 5 or greater, round the ten thousand's place digit up by 1. 5. Since the thousand's place digit is 6 (which is greater than 5), we round the 9 in the ten thousand's place up by 1. 6. Increasing 9 by 1 gives 10, so we carry over to the hundred thousand's place. 7. Therefore, 196725 rounded to the nearest ten thousand is 200000. **Final answer:** $200000$