Depth · one concept from first principles · step 2 of 4
Using each of the number cards exactly once, you form the five-digit number that is closest to . Round that five-digit number to the nearest hundred.
Number cards: , , , ,
Below 30000 the leading digit must be 2, so fill the rest largest-first to reach 29730.
A bigger digit in the thousands place pushes the number up toward 30000, so I greedily use my largest leftover digits first.
4.NBT.A.1Guess And CheckAt or above 30000 the leading digit is 3, so fill the rest smallest-first to reach 30279.
A smaller digit right after the 3 keeps the number low, so I greedily use my smallest leftover digits first.
4.NBT.A.1Guess And CheckThe two gaps are 270 and 279, so 29730 is the closer of the pair.
Closest means the smallest distance, so I just compare the two gaps and pick the smaller one.
4.NBT.A.2Make A Systematic List29730 sits closer to 30000 than 30279 does.
How far a number sits from 30000 is the stretch you have to cross to reach it, and that stretch is what taking the smaller number from the larger one measures.
Both gaps are measured the same way, so the smaller gap belongs to the nearer number.
Each unit of gap matches one step along the number line, so fewer units is a shorter walk.
The tens digit 3 is under 5, so 29730 rounds down to 29700.
Rounding to the nearest hundred looks only at the tens digit: 3 is below halfway (5), so the hundreds digit stays the same.
3.NBT.A.1Guess And CheckThe number nearest a target can be just below it, so always check both the biggest 'just-under' and the smallest 'just-over' number.
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