A convert card reads "350 cm → ↓÷100 → 3.5 m": it always shows the ×n or the ÷n. One card's result can feed the next, so cm → m → km runs as a relay.
How to read this board
The point of it is that the convert card does not hide the factor. A tool that only produces answers would stop at "3.5 m", and you would stop at the same place again next time. With the ÷100 in view, the reverse direction is obviously ×100.
The relay is there for the same reason. cm → m is ÷100, then m → km is ÷1000. Split in two, there is no ÷100000 to remember.
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 |
|---|---|---|
| A bigger unit gives a smaller number | "Make it bigger" and "the digits shrink" pull in opposite directions. | The cm → m card shows ÷100. The unit is 100 times larger, so the count is one hundredth. |
| Which way to apply the factor | Remember only the factor and you have to re-derive the direction every time. | The card prints × or ÷ for the direction it is set to. Swap from and to with the ⇄ button and the display flips to ×100. |
| Area and volume work in squares and cubes | 1 m = 100 cm, so 1 m² looks like it should be 100 cm². It is 10,000 cm². | The area card shows ×10,000 — an order of magnitude away from the ÷100 and ×100 of the length cards. |
| Time does not run in tens | Lengths and masses convert by 10, 100 and 1000; time runs on 60 minutes to an hour, 60 seconds to a minute. Carry the decimal habit across and 142 minutes becomes "1.42 hours". | Convert 142 minutes into hours. It is 2.366… hours, not 1.42. |
| Currency is not on the card | It looks like a unit conversion, but a rate changes daily and does not sit in the same mechanism. | There is no currency in the card. For an exchange rate, type the rate in yourself and multiply with a calculation card. |
Converting a unit is asking how the same quantity reads on a different scale. What is hard is not the arithmetic but keeping track of which side is the reference. Leave the factor in the formula and the direction, and the size of the step, stay readable.
Try this
- 2500 cm into m, then into km — 25 m, then 0.025 km. Because it is two steps, where the 100 went and where the 1000 went are both still on the screen.
- Press ⇄ to reverse a card — ÷100 becomes ×100. No mental inversion required.
- 12 m² into cm² — 120,000 cm². Reach for the length factor of 100 and you would answer 1,200 cm². Same cm and m; in area the factor is 10,000.