Concept 1 of 6
The Millionaire's Mansion: The Place Value Hierarchy
Today's big idea
Where a digit sits decides what it is worth, and each room left is 10 times bigger.
Same digit twice: the 3 in thousands is worth 3,000, the 3 in tens just 30.
How it works
👀 What's going on?
Your school raised 3,535 rupees at the fair. Two of those digits are 3s, and they look identical. One of them is worth a hundred times more than the other. That is the whole trick of our number system, and it is why 3,535 is not the same as 5,353.
💡 Here's the trick
Look at the mansion above. The 3 in the thousands room is worth 3,000. The other 3, over in the tens room, is worth only 30. A digit's room decides its value, and each room to the left holds 10 times more than the room on its right.
🪄 How to do it
- 1.Name the rooms in the picture above from the right: ones, tens, hundreds, thousands.
- 2.Find your digit and read off which room it is sitting in.
- 3.Multiply the digit by that room's value to get what it is worth.
✍️ Try it
The number 2,858,000 also has a repeated digit. What is each 8 worth?
The first 8 sits in the hundred-thousands room, so it is worth 800,000. The other 8 sits in the thousands room, so it is worth 8,000. One is a hundred times the other, from the same digit.
⚠️ Watch out
You might be thinking a bigger digit always makes a bigger number. Compare 4,000 with 900. The 9 is the bigger digit, but 900 is the smaller number. The room beats the digit every time.
🌟 Why this matters
Reading a price tag, a cricket score, or the population of your city all start here. Get the rooms wrong and 25,000 rupees turns into 2,500, which is the kind of slip that costs real money.
Exam tip: Nearly every other idea in this chapter is built on rooms, so this is the one to be solid on.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“What is the value of the 4 in 4,572?”
- 1
Find which room the 4 lives in
4,572 — the 4 sits in the THOUSANDS room. 🏠
- 2
Look up the room's value
The Thousands room is worth 1,000 each.
- 3
Multiply the digit by the room
4 × 1,000 = 4,000
- 4
True value found ✓
The 4 in 4,572 is worth 4,000
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Drag the digit across the rooms. Each room left is 10× bigger — land it so it's worth exactly 5,000.
Hund-Thou
100,000
Ten-Thou
10,000
Thousands
1,000
Hundreds
100
Tens
10
Ones
1
The 5 in Ones is worth 5
Quick check
✅ VERIFICATION
In 407,650, what is the 4 actually worth?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Number Translators
Switch between '45,300' and 'Forty-Five Thousand, Three Hundred' instantly.