Depth · one concept from first principles · step 2 of 4
Carry ten units to the next place
Find the digit , where is one of the numbers from to .
In , there are thousands, hundreds, tens, and ones.
Base-ten numbers
Your answer
Watch out The question asks for the hundreds digit, not the 4 that sits in the tens place.
How to solve
Strategy Draw a Diagram — Reading a number by its place values is a direct place-value chart task, so I line up the digits of 7545 with the thousands, hundreds, tens, and ones positions to read off the hundreds digit.
1STEP 1
Line up the digits with their places
In a place-value chart: 7 goes in thousands, the first 5 in hundreds, 4 in tens, and the last 5 in ones.
7545 = 7000 + 500 + 40 + 5
Each digit's spot in the number tells you exactly which place it counts, like columns on a chart.
4.NBT.A.1Draw A DiagramThe 5 sitting in the hundreds place of 7545 counts exactly 5 hundreds.
Why?
Where a digit sits decides how much it is worth, and the spot third from the right is the hundreds spot, so the 5 written there counts 5 hundreds.
Why?
That spot is the hundreds spot because each place is worth ten of the place on its right — ten ones make one ten and ten tens make one hundred — so counting ones, then tens, then hundreds lands the hundreds two steps left of the ones.
🧱Place-value groupingTen ones make one ten and ten tens make one hundred — each place bundles ten of the last.
2STEP 2
Read the hundreds digit
The digit in the hundreds place is 5, so 7545 has 5 hundreds — that means ■ = 5.
■ = 5
The hundreds count is simply the digit in the hundreds column.
4.NBT.A.2Look For A PatternAnswer
5
Rebuild the number: 7 thousands + 5 hundreds + 4 tens + 5 ones = 7000 + 500 + 40 + 5 = 7545, which matches, so ■ = 5 is correct.
Takeaway
Each digit lives in its own place column, so the hundreds count is just the digit standing in the hundreds spot!
- Line up the digits with their places
- Read the hundreds digit
Where next?
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A parent dashboard for the family lives at sensimlab.com.
The same shape shows up later on the AMC, as Arithmetic Expression Decomposition, Casework by Position / Vertex Type. Why the shapes repeat →