Answer :
We want to round [tex]$82,\!649$[/tex] to the nearest ten thousand. Follow these steps:
1. Write the number in a form that highlights the ten thousands place:
[tex]$$82,\!649 = 8.2649 \times 10^4$$[/tex]
2. Look at the digit in the thousands place (the digit immediately after the ten thousands place). In [tex]$82,\!649$[/tex], the thousands digit is [tex]$2$[/tex].
3. Apply the rounding rule:
- If the digit in the thousands place is less than [tex]$5$[/tex], round down.
- If it is [tex]$5$[/tex] or greater, round up.
Since [tex]$2 < 5$[/tex], we round down.
4. Rounding down means the ten thousands digit remains [tex]$8$[/tex], and all lower place values become [tex]$0$[/tex]. Thus:
[tex]$$82,\!649 \text{ rounded to the nearest ten thousand is } 80,\!000.$$[/tex]
Therefore, the final answer is [tex]$\boxed{80,\!000}$[/tex].
1. Write the number in a form that highlights the ten thousands place:
[tex]$$82,\!649 = 8.2649 \times 10^4$$[/tex]
2. Look at the digit in the thousands place (the digit immediately after the ten thousands place). In [tex]$82,\!649$[/tex], the thousands digit is [tex]$2$[/tex].
3. Apply the rounding rule:
- If the digit in the thousands place is less than [tex]$5$[/tex], round down.
- If it is [tex]$5$[/tex] or greater, round up.
Since [tex]$2 < 5$[/tex], we round down.
4. Rounding down means the ten thousands digit remains [tex]$8$[/tex], and all lower place values become [tex]$0$[/tex]. Thus:
[tex]$$82,\!649 \text{ rounded to the nearest ten thousand is } 80,\!000.$$[/tex]
Therefore, the final answer is [tex]$\boxed{80,\!000}$[/tex].
