Concept 4 of 6
The Vertical Stack: Comparing Giant Numbers
Today's big idea
Stack the numbers and scan left to right, because the first column that differs wins.
23,481 against 23,471: all matches until the tens, where 8 beats 7.
How it works
👀 What's going on?
Which is bigger, 23,481 or 23,471? At a glance they look like the same number printed twice. Stacking them turns that squint into a five-second check.
💡 Here's the trick
Look at the stack above. The ten-thousands, thousands and hundreds columns all match, so none of them decides anything. The first column that differs is the tens, where 8 beats 7. That single column settles it, and 23,481 wins no matter what follows.
🪄 How to do it
- 1.Stack the numbers so their right-hand edges line up, as in the picture above.
- 2.Count the digits first, because more digits always wins.
- 3.If the counts match, walk left to right and stop at the first column that differs.
✍️ Try it
Compare 9,999 with 10,002. Then compare 47,309 with 47,390. What decides each one?
9,999 has four digits and 10,002 has five, so 10,002 wins before you compare a single column. For the second pair the counts match, so walk left. The 4, 7 and 3 all agree, then the tens differ, 0 against 9, so 47,390 is bigger.
⚠️ Watch out
You might be thinking the number starting with the biggest digit wins. 9,999 opens with a 9 and still loses to 10,002. Count the digits before you compare any of them.
🌟 Why this matters
Sorting a leaderboard, comparing two phone prices, or checking which city holds more people all run on this. Working left to right means you can stop the moment you know, instead of reading every digit.
Exam tip: Ordering questions almost always slip in one pair of different lengths, and that pair is the fastest mark on the page.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Which is bigger: 71,608 or 71,590?”
- 1
Stack them by place value
Line up the right edges so digits match: 7-1-,-6-0-8 over 7-1-,-5-9-0.
- 2
Scan left to right
Ten-thousands match (7 = 7). Thousands match (1 = 1).
- 3
Spot the first difference
Hundreds: 6 vs 5 — they're different!
- 4
Bigger digit wins ✓
6 > 5 → 71,608 is bigger
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Stack the numbers, then tap the first column (from the left) where the digits are different.
Two giant numbers to compare:
145,299
vs
145,301
Quick check
✅ VERIFICATION
Which of these is the greatest: 8,999, 12,300, or 9,050?
⚡ Finish the activity above first to answer.
Keep going!
Up next: The Target and the Neighbour
Find the nearest friendly number using the neighbour digit rule.