Decimals and Rounding on a Number Line

1. 1Between Two Tenths4.37 sits between 4.3 and 4.4 on the line. It is clearly not in the middle — but eyeballing is not measuring.4.37 is between 4.3 and 4.4
2. 2Zoom Into the GapMove in close on the little gap between 4.3 and 4.4. Now every hundredth has its own tick, from 4.3 all the way up to 4.4.Ticks every 0.01 from 4.3 to 4.4
3. 3The Halfway MarkExactly halfway between 4.3 and 4.4 stands 4.35. Anything past it belongs to 4.4; anything before it belongs to 4.3. Find which side our pin is on.Halfway: 4.35
4. 4Measure Both DistancesFrom 4.37 back to 4.3 is 0.07; from 4.37 forward to 4.4 is 0.03. One segment is visibly shorter.0.07 vs 0.03
5. 5The Nearest Neighbour Wins0.03 beats 0.07, so 4.37 is nearer to 4.4. Rounded to one decimal place: 4.37 ≈ 4.4.4.37 ≈ 4.4
6. 6Read the Rule Off the PictureLook at the first dropped digit, 7, and compare it with the halfway digit 5 — the digit rule is a shortcut for this distance picture.First dropped digit: 7
7. 7Check and the Golden RuleCheck the distances once more: 4.37 − 4.3 = 0.07 and 4.4 − 4.37 = 0.03; 0.03 is smaller, so 4.4 is right.0.03 < 0.07 ✓

Change the numbers to test the engine with any sum & difference problem: