You know where numbers sit on a number line (numbers on a number line) and what each digit is worth (hundreds, tens and ones). Rounding uses both. It swaps a number for the closest ten or hundred, so it is easy to think with.
Why it works
Rounding asks one question: which ten (or hundred) is closer? The ones digit tells you how many steps you are past the lower ten. With 0 to 4 steps you are closer to the lower ten. With 6 to 9 you are closer to the upper ten. A 5 is exactly halfway, and everyone agrees to round a halfway number up.
Key idea
To round to the nearest ten, look at the ones digit. To round to the nearest hundred, look at the tens digit. 0 to 4: round down. 5 to 9: round up.
Worked example: Nearest ten
Round $247$ to the nearest ten.
- $247$ is between $240$ and $250$.
- The ones digit is 7. That is 5 or more, so $247$ is closer to $250$.
Answer: $250$
Worked example: Nearest hundred
Round $381$ to the nearest hundred.
- $381$ is between $300$ and $400$. Halfway is $350$.
- Look at the tens digit: 8. That is 5 or more, so $381$ is past halfway.
- It rounds up to $400$.
Answer: $400$
Worked example: Right at halfway
Round $450$ and $449$ to the nearest hundred.
- $450$ is exactly halfway between $400$ and $500$. Halfway rounds up: $500$.
- $449$ has tens digit 4, so it is just short of halfway. It rounds down: $400$.
Answer: $450 \to 500$ and $449 \to 400$
Common mistake
Looking at the wrong digit. To round $463$ to the nearest hundred, some people look at the ones digit (3) and round down to $400$. Look at the digit just right of the hundreds: the tens digit, 6. So $463$ rounds to $500$. Check with distance: $463$ is 63 away from $400$ but only 37 away from $500$.
Thinking 5 rounds down because it is "in the middle." A halfway number such as $450$ or $35$ always rounds up.
Thinking 5 rounds down because it is "in the middle." A halfway number such as $450$ or $35$ always rounds up.