We the Travellers – I
Big numbers, place value, comparing, rounding off, and some fun travel puzzles, explained simply with lots of examples.
- How to read and write numbers bigger than 9,999 (up to 99,999)
- The new place called Ten Thousands (TTh)
- How to compare and arrange big numbers
- How to round off a number to the nearest 10, 100, or 1,000
- How to break numbers in different ways (expanded form and regrouping)
- Thinking puzzles that make your brain sharp!
🚌 Let’s Begin with a Journey
Last Diwali, Aarav went with his family from his village to his nani’s house. First they took an auto-rickshaw to the bus stand, then a bus to the railway station, and finally a train. On the way, Aarav’s father pointed at the big stones on the roadside that show kilometres.
“Papa, how many vehicles are on this highway every day?” Aarav asked.
“Maybe twenty-five thousand, or even more!” said Papa.
Aarav wondered, “How do I even write such a big number?” That’s exactly what we will learn now.
Travelling has changed a lot. Long ago, people walked or rode animals like horses, camels, and bullocks. People also made boats to cross rivers, and boats are thought to be one of the oldest ways humans travelled. Today we have buses, trains, aeroplanes, and even rockets! As travel grew, the numbers we use for distances, passengers, and vehicles also became bigger.
🔢 Part 1: Meet the Ten Thousands
You already know numbers up to 9,999. Let’s count in thousands and see what comes next:
1,000 → 2,000 → 3,000 → … → 8,000 → 9,000 → ?
When we add one more thousand to 9,000, we get 10,000 (ten thousand). It is the smallest 5-digit number.
10 Ones = 1 Ten · 10 Tens = 1 Hundred · 10 Hundreds = 1 Thousand · 10 Thousands = 1 Ten Thousand
The new place value chart
Let’s take a number from a railway station: 12,475 passengers travelled in one day.
| TTh (Ten Thousands) | Th (Thousands) | H (Hundreds) | T (Tens) | O (Ones) |
|---|---|---|---|---|
| 1 | 2 | 4 | 7 | 5 |
We read it as: Twelve thousand four hundred seventy-five.
More examples
| Number | TTh | Th | H | T | O | Number Name |
|---|---|---|---|---|---|---|
| 10,006 | 1 | 0 | 0 | 0 | 6 | Ten thousand six |
| 18,030 | 1 | 8 | 0 | 3 | 0 | Eighteen thousand thirty |
| 30,608 | 3 | 0 | 6 | 0 | 8 | Thirty thousand six hundred eight |
| 64,219 | 6 | 4 | 2 | 1 | 9 | Sixty-four thousand two hundred nineteen |
45867 → 45,867 | 90009 → 90,009
Read the part before the comma + “thousand”, then read the rest: 45,867 = forty-five thousand eight hundred sixty-seven.
⚖️ Part 2: Comparing and Ordering Big Numbers
At a village mela, the ticket counter sold 28,905 tickets on Saturday and 28,950 tickets on Sunday. Which day had more visitors?
Two simple steps
- Count the digits. The number with more digits is bigger. (A 5-digit number is always bigger than a 4-digit number.)
- Same number of digits? Compare place by place from the left. The first place where the digits differ decides the winner.
| TTh | Th | H | T | O | |
|---|---|---|---|---|---|
| Saturday | 2 | 8 | 9 | 0 | 5 |
| Sunday | 2 | 8 | 9 | 5 | 0 |
TTh, Th, and H are the same. In the Tens place, 5 > 0. So 28,950 > 28,905, and Sunday had more visitors. 🎉
Wrong! 8,990 has only 4 digits and 12,000 has 5 digits. ✅ 12,000 is bigger. Always count digits first.
Ascending order = smallest to biggest (like climbing stairs up ⬆️).
Descending order = biggest to smallest (like coming down ⬇️).
🎯 Part 3: Rounding Off (Finding the Nearest 10, 100, 1,000)
Sometimes we don’t need the exact number. We just need a number that is “close enough” and easy to say. This is called rounding off.
A bus is standing at the kilometre stone 4,738. There is a dhaba at 4,730 and another at 4,740. Which dhaba is closer?
From 4,738 to 4,740 is only 2 km, but back to 4,730 is 8 km. So the nearest ten of 4,738 is 4,740.
The easy rule
- 0, 1, 2, 3, 4 → stay down (keep that digit, make the rest zeros)
- 5, 6, 7, 8, 9 → go up (add 1 to that digit, make the rest zeros)
| Number | Nearest Ten | Nearest Hundred | Nearest Thousand |
|---|---|---|---|
| 4,738 | 4,740 | 4,700 | 5,000 |
| 6,482 | 6,480 | 6,500 | 6,000 |
| 2,995 | 3,000 | 3,000 | 3,000 |
Notice 2,995: when you go up at the tens place, the 9s “chain up” and it becomes 3,000 at every level!
🧩 Part 4: Breaking Numbers in Different Ways
Expanded form
We write a number as the sum of the value of each digit:
30,608 = 30,000 + 600 + 8
(Zeros have no value to add, so we skip them.)
Regrouping: one number, many ways
You can break a number into bigger or smaller “packets”:
- 5,342 = 5 Thousands + 3 Hundreds + 4 Tens + 2 Ones
- 5,342 = 53 Hundreds + 42 Ones
- 5,342 = 534 Tens + 2 Ones
- 5,342 = 4 Thousands + 13 Hundreds + 42 Ones
Check any one: 4,000 + 1,300 + 42 = 5,342 ✅
Money makes it easy!
Meena’s family saved ₹4,650 for a train trip.
- In ₹100 notes: 4,650 has 46 hundreds, so 46 notes (₹50 is left over).
- In ₹500 notes: 2 notes make ₹1,000, so ₹4,000 needs 8 notes. ₹500 more makes 9 notes (₹4,500), and ₹150 is left.
- In ₹10 notes: 4,650 has 465 tens, so 465 notes.
₹4,65
🚆 Part 5: Travel Speed and Big Numbers Around Us
Different vehicles cover very different distances in one hour. Walking covers just a few km, a cycle a bit more, a train can cover more than a hundred km, and an aeroplane covers hundreds of km. A spacecraft zooms through tens of thousands of km!
Example: A goods train covers 90 km in one hour. How far will it go in 7 hours at the same speed?
90 + 90 + 90 + 90 + 90 + 90 + 90 = 90 × 7 = 630 km
Example: 540 children are going on a picnic. Each minibus has 30 seats. How many minibuses are needed?
30 × 18 = 540, so 18 minibuses.
Big numbers are everywhere! Look for the number of leaves on a neem tree, the people in your town, bricks in your school wall, or runs a batter makes in a whole career. Many of these are 4-digit or 5-digit numbers.
❌ Common Mistakes to Avoid
✅ Correct: 40,065
✅ Look at the hundreds digit (4). Stay down → 3,000 is correct! But 3,550 → 4,000.
✅ Always start from the left (biggest place).
✅ For 5-digit numbers only one comma: 45,867
✏️ Practice Time
Try these on your own first, then check your answer below each question.
(b) Seventy thousand seventy
📘 NCERT Textbook Activity Help
Hints and answers for the activities in the textbook, page by page. Try each one yourself before looking at the answer!
Page 5 · Let Us Do, Q1Continue the number patterns
Hint: Find the difference between two neighbouring numbers. That is the “jump.” Keep jumping!
- (a) Jump of +111: 789, 900, 1,011, 1,122
- (b) Jump of +1,050: 2,100, then 5,250, 6,300, 7,350
- (c) Jump of +900: 8,201, 9,101, 10,001, 10,901
- (d) Jump of +100: 10,400, 10,500, 10,600, 10,700, 10,800, (10,900), 11,000
- (e) Jump of +20: 10,145, 10,165, 10,185, 10,205, 10,225, 10,245, 10,265, 10,285
- (f) Jump of +1: 10,994, 10,995, 10,996, 10,997, 10,998, 10,999, 11,000, 11,001
- (g) Jump of +2: 10,800, 10,802, 10,804, 10,806, 10,808, 10,810, 10,812
- (h) Jump of −1,001: 71,003, 70,002, 69,001, 68,000, 66,999, 65,998, 64,997, 63,996
- (i) Jump of +1,000: 84,350, 85,350, 86,350, 87,350, 88,350, 89,350, 90,350, 91,350
Numbers and number names
- 7,209: Seven thousand two hundred nine
- 10,599: Ten thousand five hundred ninety-nine
- Ten thousand seven hundred forty-three: 10,743
- 13,579: Thirteen thousand five hundred seventy-nine
- Ten thousand ten: 10,010
- Fifty-six thousand four hundred ninety-one: 56,491
- 45,045: Forty-five thousand forty-five
- 39,593: Thirty-nine thousand five hundred ninety-three
- 50,005: Fifty thousand five
- 26,050: Twenty-six thousand fifty
- 81,200: Eighty-one thousand two hundred
- Ninety thousand nine: 90,009
- Twenty-three thousand two hundred thirty: 23,230
- Thirty-six thousand one: 36,001
Increasing order
Is 9,990 greater than 49,014?
Number line boxes (jumps of 5,000): 5,000, 10,000, 15,000, 20,000, 25,000, 30,000, 35,000, 40,000, 45,000, 50,000
Digit swap
Hint: To make a number bigger, bring a big digit to the leftmost place.
- (a) Swap 1 and 8 → 8,471 (7,418 also works)
- (b) i) Swap 0 and 3 → 13,590 ii) Swap 1 and 5 → 50,193 (90,513 also works)
- (c) i) Smallest: swap the first 4 and the 2 → 28,447 ii) Biggest: swap 4 and 8 → 84,247
Help the rabbit find food
- Nearest hundred of 2,346 is 2,300, which is 46 jumps away.
- Nearest thousand of 2,346 is 2,000, which is 346 jumps away.
| Number | Nearest 10 | Nearest 100 | Nearest 1,000 |
|---|---|---|---|
| 3,176 | 3,180 | 3,200 | 3,000 |
| 4,017 | 4,020 | 4,000 | 4,000 |
| 5,789 | 5,790 | 5,800 | 6,000 |
| 8,203 | 8,200 | 8,200 | 8,000 |
Rounding puzzles
- Q1: Circle 7,030 and 6,999. Both round to 7,000 at the hundred and at the thousand level. (7,126 → 7,100 and 7,000; 7,835 → 7,800 and 8,000, which don’t match.)
- Q2 (sample answers): (a) 38 and 43 → both 40 (b) 260 and 340 → both 300 (c) 1,700 and 2,300 → both 2,000
- Q3 (sample answers): (a) 298 → 300 and 300 (b) 4,960 → 5,000 and 5,000 (c) 2,998 → 3,000 at ten, hundred, and thousand
Cyclist and school trip
Q1: 15 km × 4 = 60 km
Q2: Total students = 461 + 439 = 900. Divide 900 by the seats in each vehicle:
| Vehicle | Seats | Vehicles needed |
|---|---|---|
| Bicycle | 2 | 450 |
| Autorickshaw | 3 | 300 |
| Car | 4 | 225 |
| Big car | 6 | 150 |
| Tempo traveller | 10 | 90 |
| Boat | 20 | 45 |
| Minibus | 25 | 36 |
| Aeroplane | 180 | 5 |
Pages 10–11 ask you to find big numbers in your school, classroom, a tree, and your town. Those answers depend on where you live, so go explore and count!
River crossing puzzle
Hint: The sheep is the “problem animal.” It can’t be left with the lion or with the grass.
- Take the sheep across. Come back alone.
- Take the lion across. Bring the sheep back.
- Take the grass across (it stays with the lion, which is safe). Come back alone.
- Take the sheep across again. Done! ✅ (7 crossings)
Pile of pebbles game
The magic 9 puzzle
- What’s common? Every difference (36, 27, 45, 9…) is in the table of 9.
- Relationship: Difference of the numbers = 9 × (difference of the digits). For example, 7 − 3 = 4, and 9 × 4 = 36.
- 1-digit answer in the first step: Choose digits next to each other, like 4 & 5, 6 & 7, or 2 & 3. Their gap is 1, so the difference is 9.
- Difference 27: Digits with a gap of 3, like 1 & 4, 2 & 5, or 6 & 9.
- Extend the table: gap 2 → 3 & 5 (53 − 35 = 18); gap 3 → 1 & 4 (41 − 14 = 27); gap 5 → 2 & 7 (72 − 27 = 45); gap 7 → 1 & 8 (81 − 18 = 63)
- 1-digit number in the third subtraction: digits with a gap of 3 or 8, like 1 & 4 (27 → 45 → 9) or 1 & 9 (72 → 45 → 9)
- Most subtractions: digits with a gap of 2, like 3 & 5: 18 → 63 → 27 → 45 → 9 (5 subtractions)
Comparing, ordering, expanded form
- Q1 (sample): 23,600, 23,750, 23,900, 24,000, 24,100
- Q2 (sample): 38,200, 38,300, 38,400, 38,450, 38,500
- Q3: Sheetal’s car (67,543 > 56,987)
- Q4: ₹39,999 < ₹49,900 < ₹89,999 < ₹90,000 < ₹93,743 < ₹94,983
- Q5: Town 6 (66,540), Town 1 (65,232), Town 3 (56,380), Town 2 (53,231), Town 4 (51,336), Town 5 (45,858)
- Q6: 43,000, 44,000, 45,000, 46,000, 47,000, 48,000, 49,000, 50,000, 51,000, 52,000, 53,000
- Q7: 8,062 = 8,000 + 60 + 2 · 9,980 = 9,000 + 900 + 80 · 10,304 = 10,000 + 300 + 4 · 23,004 = 20,000 + 3,000 + 4 · 70,405 = 70,000 + 400 + 5
Regrouping
Hint: Work out what’s already given, subtract it from the number, and see what’s left.
- (b) 68 = 5 Tens + 18 Ones
- (c) 607 = 4 Hundreds + 207 Ones
- (d) 5,621 = 4 Thousand + 16 Hundreds + 2 Tens + 1 One
- (e) 7,069 = 5 Thousand + 20 Hundreds + 69 Ones
- (f) 37,608 = 2 Ten Thousand + 17 Thousand + 6 Hundreds + 8 Ones
- (g) 43,001 = 3 Ten Thousand + 13 Thousand + 0 Hundreds + 1 One
Notes and thousands
- (b) 79 notes of ₹100 (c) 7 thousands (d) 15 notes of ₹500 (2 per thousand → 14, plus one more for ₹500)
- (e) 6,534 notes of ₹10 (f) 653 notes of ₹100 (g) 65 thousands (h) 130 notes of ₹500
Where did the caretaker cheat?
Hint: Look at the horses standing in the corner rooms. How many sides do they belong to?
Count one by one: there were only 19 horses. The trick is that a horse in a corner room gets counted on two sides. So the corners were counted twice.
18 horses with 5 on each side: Put 1 horse in two opposite corners (top-left and bottom-right), and 2 horses in each of the 8 middle rooms. Each side = 1 + 2 + 2 = 5, and the total is 2 + 16 = 18. ✅
How many more can be stolen? Put all horses in the corners: 5 in the top-left corner and 5 in the bottom-right corner. Every side still shows 5, but there are only 10 horses! So the thief can steal 8 more (from 18 down to 10) before the king notices.
👨👩👧 Tips for Parents
- On a trip, ask your child to read kilometre stones and vehicle numbers aloud.
- Show prices of phones, bikes, or TVs in an ad and ask, “Which is costlier? Round it to the nearest thousand.”
- Play “number bank” with toy notes: How many ₹100 notes make ₹3,400?
- Try the river crossing and pebble games at home. They build logical thinking.