Change the town population and all four cards move at once: to the nearest hundred, to the nearest thousand, rounded down and rounded up.
How to read this board
roundto(number, 2) means 102 — round to the nearest hundred. The
second argument names a place, not a count of digits.
floorto rounds down, ceilto rounds up.
The four sit in a row so that one number, 34,567, can be seen producing 34,600 to the nearest hundred, 35,000 to the nearest thousand, 34,000 rounded down at the same moment. Rounding to the nearest thousand and rounding up both give 35,000 here — different methods land on the same answer often enough to be misleading.
Where it trips you up
The places that are easy to get wrong, next to how to check each one on the board.
| Where it trips you up | Why that happens | How the board shows it |
|---|---|---|
| "2 significant figures" is not "to the nearest hundred" | Both involve a 2, so they blur together. One counts digits kept, the other names a place. | 34,567 to 2 significant figures is 35,000; to the nearest hundred it is 34,600. Two cards, two answers. |
| Which digit you actually look at | Asked for the nearest thousand, it is tempting to stare at the thousands digit. The one that decides is the place below it. | Put the hundreds card and the thousands card side by side, then change the last three digits and watch which one moves. |
| Rounding up or down is a decision about the situation | The arithmetic does not settle it. "How many do I need to buy" rounds up; "how many fit" rounds down. | Both cards are on the board at once. Which one applies comes from outside the board, so seeing both is the correct state. |
| Rounding first makes the error grow | Round, then add, and you drift away from adding first and rounding at the end. | Feed the rounded card into another calculation and compare it against the same calculation from the original number. |
| Where a half goes | An exact half has to go somewhere, and that is a convention rather than a mathematical necessity. Common practice sends it up; some fields send it to the nearest even digit instead, to stop a long column of numbers drifting upward. | Type 34,500 in. roundto on this board sends the half up. |
| The zeros hide the size | 35,000 and 3,500 look alike at a glance, and a rounded number is easy to misread by a factor of ten. | The board keeps the original next to the rounded versions, so the digit counts can be compared by eye. |
A rounded number is settled by two choices: which place you keep and which method you use. Calling 34,567 people "35,000" is a decision to throw the last three digits away. Keeping the original beside the result shows which digits the answer actually turned on.
Try this
- Change 34,567 to 34,499 — to the nearest thousand it drops from 35,000 to 34,000. A difference of 68 becomes a difference of 1,000 once it is written down.
- Keep moving the place up — hundreds, thousands, ten thousands: the higher you go the more of the original disappears. How much you may throw away depends on what the number is for.
- Compare rounding down against rounding up — 34,000 against 35,000 at the thousands. "Approximately" covers a range of 1,000 here, which is worth knowing before you quote it.