Numbers — Class 4 Mathematics (Samacheer Kalvi)
TN State Board (Samacheer Kalvi) Class 4 Mathematics, Unit 2. Number sequence up to 10,000, comparing and ordering numbers, addition and subtraction. Taught in June and July.
1. Numbers up to 10,000
In Class 3 you worked with hundreds. This year the numbers get one column longer.
Look at how a real announcement uses them. The transport department ran about 10,000 special buses for Diwali. Of 9,967 special services, 6,367 ran from Chennai to other districts and 3,600 ran within the districts.
To hold a four-digit number we need four places on the abacus. Reading from the right: O (ones), T (tens), H (hundreds), Th (thousands).
| Th | H | T | O | Number |
|---|---|---|---|---|
| 4 | 0 | 0 | 0 | 4000 |
| 5 | 4 | 8 | 3 | 5483 |
| 9 | 0 | 2 | 0 | 9020 |
2. Expanded form and number names
The expanded form splits a number into what each digit is worth.
534 = 500 + 30 + 4, read as five hundred thirty four.
Write the number name of 1283. First expand it, then name each part and join them up:
1283 = 1000 + 200 + 80 + 3 = One thousand + Two hundred + Eighty + Three
So 1283 is one thousand two hundred and eighty three.
This matters outside the classroom. When Ramu deposits ₹7,500 at a bank, the challan asks him to write the amount in words — seven thousand five hundred.
3. Place value and face value
Here is the distinction children lose marks on. The face value of a digit is just the digit itself, wherever it sits. The place value depends on the column it stands in.
Take the number 5269:
| Digit | Place | Value |
|---|---|---|
| 5 | Thousands | 5000 |
| 2 | Hundreds | 200 |
| 6 | Tens | 60 |
| 9 | Ones | 9 |
The face value of 5 is always 5. Its place value here is 5000, because it sits in the thousands column. Move the same 5 into the tens column and its place value drops to 50.
4. Odd and even numbers
A number is even if it ends in 0, 2, 4, 6 or 8, and odd if it ends in 1, 3, 5, 7 or 9. Only the ones digit decides. So 8123 is odd (ends in 3) and 5920 is even (ends in 0), no matter how long the number is.
5. Making the biggest and smallest number
Given some digits, you can arrange them into many numbers. Two of those are worth naming.
To make the largest number, put the digits in descending order — biggest digit first. To make the smallest number, put them in ascending order — smallest digit first.
The smallest 4-digit number using 4, 2, 9 and 7 once each is 2479.
The zero trap. A number cannot begin with 0, or it stops being a four-digit number. So when zero is one of your digits, lead with the smallest digit that is not zero, then put the zero next, then the rest in ascending order. Using 5, 0, 9 and 3, the smallest is 3059, not 0359.
6. Ascending and descending order
Ascending order runs from smallest to biggest. Descending order runs from biggest to smallest.
To compare four-digit numbers, start at the thousands column and work rightwards. Stop at the first column where they differ.
Order 4278, 4875, 4923 and 4717. Every one of them has 4 thousands, so the thousands tell us nothing. Move to the hundreds: 2, 8, 9, 7. That settles it.
Ascending: 4278 < 4717 < 4875 < 4923.
7. Addition
Two facts to keep:
- Adding 0 changes nothing. 5349 + 0 = 5349.
- Adding 1 gives the next number. 3457 + 1 = 3458.
Addition with regrouping. When a column adds to 10 or more, carry the extra into the next column.
Find the sum of 1957, 2376 and 4697:
| Th | H | T | O |
|---|---|---|---|
| 1 | 9 | 5 | 7 |
| 2 | 3 | 7 | 6 |
| 4 | 6 | 9 | 7 |
| 9 | 0 | 3 | 0 |
The answer is 9030.
Two results worth memorising: 9999 + 1 = 10,000, and the greatest 3-digit number plus the smallest 4-digit number is 999 + 1000 = 1999.
8. Subtraction
Without regrouping, each digit on top is big enough to subtract from:
9865 − 2334 = 7531.
Roja earns ₹8,950 a month and spends ₹6,750. Her saving is 8950 − 6750 = ₹2,200.
With regrouping, a digit on top is too small, so you borrow from the column to its left. Subtract 3285 from 5657. In the tens column 5 is less than 8, so borrow one hundred, making it 15 tens and leaving 5 hundreds:
5657 − 3285 = 2372.
Finding a missing number. The sum of two numbers is 4204 and one of them is 1207. Subtraction undoes addition, so the other number is 4204 − 1207 = 2997.
9. Multiplication
Multiplying by a two-digit number is done in two rounds, one for the ones digit and one for the tens digit.
Work out 45 × 32:
- Multiply by the ones digit: 45 × 2 = 90
- Multiply by the tens digit: 45 × 30 = 1350
- Add the two results: 90 + 1350 = 1440
The second line is where marks are lost. Because you are multiplying by a tens digit, the answer must start in the tens column, so write a 0 in the ones place first and then multiply by 3. That placeholder zero is what keeps the place value honest.
The same method handles a three-digit number: 324 × 7 = 2268.
10. Division
Long division works from the left, one digit at a time. Divide 876 by 5:
- 5 into 8 goes 1 time (1 × 5 = 5), remainder 3
- Bring down the 7 to make 37. 5 into 37 goes 7 times (7 × 5 = 35), remainder 2
- Bring down the 6 to make 26. 5 into 26 goes 5 times (5 × 5 = 25), remainder 1
So 876 ÷ 5 = 175 remainder 1.
Check any division by multiplying back: 175 × 5 = 875, and 875 + 1 = 876.
11. Rounding
Rounding replaces a number with a nearby round number that is easier to handle. Look at the digit just after the place you are rounding to. If it is 5 or more, round up; if it is 4 or less, round down.
| Number | To nearest 10 | To nearest 100 | To nearest 1000 |
|---|---|---|---|
| 4,832 | 4,830 | 4,800 | 5,000 |
| 2,567 | 2,570 | 2,600 | 3,000 |
Rounding is how you check an answer quickly. If 45 × 32 is roughly 50 × 30 = 1500, then 1440 is believable but 14,400 is not.
12. Worked examples
Example 1. Write 6785 in expanded form.
Solution: 6785 = 6000 + 700 + 80 + 5.
Example 2. What is the place value of 5 in 3758?
Solution: 5 sits in the tens column, so its place value is 50.
Example 3. Write the numeral for "seven thousand and sixty four".
Solution: 7000 + 60 + 4 = 7064. The hundreds place gets a 0.
Example 4. Form the greatest and smallest 4-digit numbers using 1, 4, 3 and 7.
Solution: Greatest = 7431 (descending). Smallest = 1347 (ascending).
Example 5. Add 2713 + 104 + 1172 + 4010.
Solution: 2713 + 104 = 2817; 2817 + 1172 = 3989; 3989 + 4010 = 7999.
Example 6. A man bought a bed for ₹2,100, a dining table for ₹3,500 and six chairs for ₹3,200. How much did he pay?
Solution: 2100 + 3500 + 3200 = ₹8,800.
Example 7. Write 3435, 3670, 139, 3267 and 6544 in descending order.
Solution: 6544 > 3670 > 3435 > 3267 > 139.
13. Practice
- Write 4,206 in expanded form.
- What is the place value of 8 in 4,832?
- Write the number name of 5,073.
- Circle the odd numbers: 9001, 8002, 7603, 6542, 4875.
- Form the greatest and smallest 4-digit numbers using 6, 7, 1 and 5.
- Arrange 2715, 2175, 2517 and 2157 in ascending order.
- Add 216 + 3422 + 4019 + 497.
- Subtract 1348 from 3445.
- The sum of two numbers is 7036 and one is 3168. Find the other.
- Multiply 56 × 43.
- Divide 543 by 6 and give the remainder.
- Round 4,832 to the nearest hundred.
- Multiply 408 × 5.
14. Answers
- 4000 + 200 + 0 + 6 = 4000 + 200 + 6.
- 8 is in the hundreds column, so its place value is 800.
- Five thousand and seventy three.
- 9001, 7603, 4875.
- Greatest 7651; smallest 1567.
- 2157 < 2175 < 2517 < 2715.
- 216 + 3422 = 3638; + 4019 = 7657; + 497 = 8154.
- 3445 − 1348 = 2097.
- 7036 − 3168 = 3868.
- 56 × 3 = 168; 56 × 40 = 2240; total 2408.
- 543 ÷ 6 = 90 remainder 3, since 90 × 6 = 540.
- 4,800 — the tens digit is 3, so round down.
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15. Summary
- Four-digit numbers use the places Th, H, T, O; the largest this year is 10,000.
- Expanded form splits a number by place: 1283 = 1000 + 200 + 80 + 3.
- Face value is the digit itself; place value depends on the column. In 5269 the 5 is worth 5000.
- Even numbers end in 0, 2, 4, 6, 8; odd numbers end in 1, 3, 5, 7, 9. Only the ones digit matters.
- Descending digits make the largest number; ascending digits make the smallest — but a number may never start with 0.
- Compare from the thousands column rightwards, stopping at the first column that differs.
- Regroup in addition by carrying; regroup in subtraction by borrowing.
- Subtraction undoes addition, so a missing addend is found by subtracting.
