CBSE Class 3 · Mathematics
Double Century
Official NCERT chapter from Maths Mela (book code cemm1). ExamMaster notes are original teaching at CBSE Class 3 depth.
This lesson follows the official chapter “Double Century” in Maths Mela. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.
- CBSE Class 3
- Easy level
- 8 concepts
1People first kept counts as marks, not digits
A mark for each thing is a count you can see. Digits came later as a shorter record of the same last word.
A digit without knowing what it stands for is a drawing, not a count.
Figure. A mark for each thing is the count you can see. The digit 5 is a shorter record of those five marks, not a new kind of number.
How it works
- Make one mark eachHonest one-to-one.
- Read the last wordThat is the size.
- Later, write a digitThe digit stores that word.
2A bundle of ten marks is a new house
Ten ones are traded for one ten. That ten lives in a new house to the left of ones.
Nine marks are not yet a ten. Do not force the trade.
Figure. Ten ones trade for one ten. That ten lives in a new house to the left of ones. Nine marks are not yet a ten.
How it works
- Fill ten onesA finished bundle.
- Trade for one tenNew house.
- Leave leftovers in onesNot a fake ten.
3Hundred is ten tens; two hundred is a double century
Ten tens make one hundred. Two such hundreds are two hundred — a double century of ones.
“Century” here is the hundred-bundle, not a cricket story you invent later.
Figure. Ten tens make one hundred. Two such hundreds are two hundred — a double century of ones. The hundreds house shows 2.
How it works
- Bundle ten tensThat is 100.
- Take two of those200.
- Say two hundredsThe hundreds house shows 2.
Double century from tens
How many ones sit in two hundreds?
- One hundred10 tens = 100 ones
- Two hundreds2 × 100
- Ones200
Pro tip. A double century is two finished hundred-bundles.
4Read a three-digit number by houses
368 is 3 hundreds, 6 tens, 8 ones. Read left to right: hundreds house first.
Mixing the houses — calling it 3 tens — breaks the read.
Figure. 368 is 3 hundreds, 6 tens, 8 ones. Read left to right: hundreds house first. Mixing the houses breaks the read.
How it works
- Point to hundredsThe left digit.
- Then tensThe middle digit.
- Then onesThe right digit.
5Compare from the hundreds house first
412 and 389: hundreds 4 against 3 decides. You do not need the ones yet.
Comparing ones first can lie when the hundreds differ.
Figure. 412 against 389: hundreds 4 against 3 decides. You do not need the ones yet. Comparing ones first can lie when the hundreds differ.
How it works
- Look at hundredsDifferent? Stop there.
- If equal, look at tensNext house.
- If still equal, look at onesLast house.
6A number can be split without changing its value
200 = 100 + 100. 130 = 100 + 30. The total stays; only the split changes.
A split that loses a house is a different number.
Figure. 200 = 100 + 100. The total stays; only the split changes. A split that loses a house is a different number.
How it works
- Fix the totalDo not change how many.
- Open one house into smaller housesHundreds into tens.
- Check the sumParts must rebuild the total.
7Zero holds a house open
In 205 the 0 says “no tens”, but the ones still sit in the ones house. Without zero, 25 would be a different number.
Zero is a holder, not a skip of the house.
Figure. In 205 the 0 says “no tens”, but the ones still sit in the ones house. Dropping the zero writes 25 — a different number.
How it works
- Read each houseHundreds, tens, ones.
- If a house is emptyWrite 0 there.
- Do not drop the houseDropping it moves the digits.
8The story of numbers is why the houses exist
Houses exist so a large count can be written with ten digits. The story is the reason for place; it is not a replacement for reading the houses.
A tale without a house-read is history class, not the number.
Figure. Houses exist so a large count can be written with ten digits. Ten of a house make the next. The story explains; the houses name the number.
How it works
- Remember why we bundleTen of a house make the next.
- Then read this numberHouses first.
- Keep story and read apartStory explains; houses name.
205 without the zero written would be confused with
- 25, a different number
- The same 205
- 200 + 5 written as 25
Zero holds the tens house open.
Notes
- The official chapter title is “Double Century”. Teach the school test for that title, not a contest shortcut.
- If a step needs a later class, stop. The next official chapter will pick it up.
Formulas
- 100 = 10 tens.
- 200 = 2 hundreds (a double century of ones).
- A three-digit number is (hundreds\times 100) + (tens\times 10) + ones.
Reference tables
Read left to right. Each digit names its house.
| Hundreds | Tens | Ones | Number |
|---|---|---|---|
| 3 | 6 | 8 | 368 |
| 2 | 0 | 5 | 205 |
| 1 | 0 | 0 | 100 |
| 2 | 0 | 0 | 200 |
Recap
Hold these pegs from the official chapter “Double Century”. The wording is ExamMaster’s teaching, not a textbook recap.
- People first kept counts as marks, not digits
- A mark for each thing is a count you can see.
- A bundle of ten marks is a new house
- Ten ones are traded for one ten. That ten lives in a new house to the left of ones.
- Hundred is ten tens; two hundred is a double century
- Ten tens make one hundred. Two such hundreds are two hundred — a double century of ones.
- Read a three-digit number by houses
- 368 is 3 hundreds, 6 tens, 8 ones. Read left to right: hundreds house first.
- Compare from the hundreds house first
- 412 and 389: hundreds 4 against 3 decides.
- A number can be split without changing its value
- 200 = 100 + 100. 130 = 100 + 30. The total stays; only the split changes.
Practise Double Century
Reading is free and needs no account. Practice, mocks and progress live in the app.
- A 4-question practice set that ends the chapter
- 1 quick check with worked explanations
- Timed mocks scored with the real marking scheme
- Readiness tracked per topic, kept on your device