In Grade 3 you learned rounding to the nearest 10 or 100. The same idea works for any place: find the two "round" numbers on either side, and pick the closer one.
Key idea
To round to a place, look at the digit just to its right. If it is 5 or more, round up; if it is less than 5, round down. The rounding digit stays or goes up by 1, digits to its left stay the same, and every digit to its right becomes 0.
Why it works
Rounding to the nearest thousand asks: which thousand is closer? $46{,}372$ sits between $46{,}000$ and $47{,}000$. The halfway point is $46{,}500$. The hundreds digit tells you which side of halfway you are on: 3 hundreds is less than 5 hundreds, so it is closer to $46{,}000$.
Worked example: Round down
Round $46{,}372$ to the nearest thousand.
- The thousands digit is 6, so the number is between $46{,}000$ and $47{,}000$.
- The digit to its right (hundreds) is 3. That is less than 5, so round down.
- Keep 46 thousands; the digits after become zeros.
Answer: $46{,}000$
Worked example: Round up through a 9
Round $39{,}682$ to the nearest thousand.
- It is between $39{,}000$ and $40{,}000$.
- The hundreds digit is 6, which is 5 or more, so round up.
- 39 thousands plus 1 thousand is 40 thousands: the 9 becomes 0 and the 3 becomes 4.
Answer: $40{,}000$
Common mistake
Rounding one digit at a time from the right: $1{,}448$ to the nearest hundred becomes $1{,}450$ and then $1{,}500$. But $1{,}448$ is closer to $1{,}400$. Only the digit just to the right of the rounding place decides, and digits to the left only change when rounding up carries (as in $39{,}682 \to 40{,}000$). Check: your answer must be the closer of the two round numbers on either side.