Concept 1 of 7
The Place Value House Grows Up: 7 & 8 Digit Numbers
Today's big idea
Each room to the left is ten times the one beside it, so value is digit times room.
A zero still holds its room open, which is why it cannot simply be dropped.
How it works
👀 What's going on?
An eight-digit number looks like a wall of digits with nothing to hold on to. It is the same place value house you have always used, just with more rooms added on the left.
💡 Here's the trick
Look at the house above. Every room is ten times the room to its right, all the way up through lakhs and crores. What a digit is worth depends entirely on which room it stands in, so the same 4 can mean four or forty lakh.
🪄 How to do it
- 1.Split the number into rooms using the house above, starting from the right.
- 2.Find which room your digit is standing in.
- 3.Multiply the digit by the size of that room.
✍️ Try it
In 6,05,39,412, what is the place value of the 6? Then: what is the place value of the 3?
The 6 stands in the crores room, so it is worth 6,00,00,000. The 3 stands in ten thousands, so it is worth 30,000.
⚠️ Watch out
You might be thinking a zero can be ignored because it is worth nothing. It is worth nothing but it holds its room open. Take the 0 out of 6,05,39,412 and everything left of it slides down a room, turning six crore into six lakh.
🌟 Why this matters
Populations, government budgets and distances between planets are all written at this size. Reading them at a glance rather than counting digits is the difference.
Exam tip: Mark the commas in before you do anything else, since the rooms then read themselves.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“What is the place value of the digit 7 in 5,72,48,103?”
- 1
Find the room
Count from the right: 3 = Ones, 0 = Tens, 1 = Hundreds, 8 = Thousands, 4 = Ten-thousands, 2 = Lakhs, 7 = Ten Lakhs, 5 = Crores. 🏛️
- 2
Look up the room's value
The Ten Lakhs room is worth 10,00,000 each.
- 3
Multiply digit × room
7 × 10,00,000 = 70,00,000
- 4
Place value found ✓
The 7 is worth 70,00,000
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap a digit card, then tap the column where it belongs!
ROUND 1 OF 3 · PLACE EACH DIGIT
4,80,63,127
Quick check
✅ VERIFICATION
In 9,08,76,543, which digit stands in the ten-lakhs place?
⚡ Finish the activity above first to answer.
Keep going!
Up next: The Indian System
Commas mark the periods, thousand, lakh, crore.