Answer :

To round the number 82,137 to the nearest ten-thousand, you need to follow these steps:

1. Identify the place you are rounding to: Since we're rounding to the nearest ten-thousand, locate the ten-thousand place in the number 82,137. In this number, the "8" is in the ten-thousand place.

2. Look at the digit to the right: The next step is to look at the digit to the immediate right of the ten-thousand place. In 82,137, this digit is "2," which is in the thousand place.

3. Apply rounding rules:
- If the digit to the right is less than 5 (which is true in this case, as "2" is less than 5), you round down, meaning you keep the ten-thousand place the same and change all the digits to the right to zero.
- If the digit had been 5 or more, you would round up, meaning you increase the ten-thousand place by one and change all the digits to the right to zero.

4. Round the number: Since the digit "2" is less than 5, round down. This means that the "8" in the ten-thousand place stays the same and all other digits become zero, leading to a rounded number of 80,000.

Hence, 82,137 rounded to the nearest ten-thousand is 80,000.

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