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Reading and Writing Large Numbers

NCERT Class 5 · Mathematics Based on NCERT Class 5 Mathematics textbook · Free CBSE study kit

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Chapter Notes

Overview
This chapter introduces students to reading and writing large numbers up to five digits (ten thousands) in the Indian place value system. It connects the concept of large numbers to real-life contexts like travel distances, population, and vehicle counts, helping students understand the need for place value charts and commas. The one big idea is that numbers are built by grouping tens, hundreds, thousands, and ten thousands, and we use place value to read, write, compare, and round them accurately.
Key Concepts (14)
Place Value Chart
A chart that shows the value of each digit in a number based on its position (Ones, Tens, Hundreds, Thousands, Ten Thousands).
e.g. In 13,520, the digit 1 is in the Ten Thousands place (value 10,000), 3 is in the Thousands place (value 3,000), 5 in Hundreds (500), 2 in Tens (20), 0 in Ones (0).
Ten Thousand (TTh)
The place value column that comes after Thousands. 10 Thousands = 1 Ten Thousand = 10,000.
e.g. In the number 45,867, the digit 4 is in the Ten Thousands place, meaning 40,000.
Comma (,) in numbers
A punctuation mark used to separate groups of three digits from the right to help read large numbers easily.
e.g. 10,000 is written with a comma after the first digit to show it is ten thousand.
Expanded Form
Writing a number as the sum of the values of its digits.
e.g. 8,062 = 8,000 + 0 + 60 + 2 (or 8 Thousands + 0 Hundreds + 6 Tens + 2 Ones).
Number Name
The word form of a number, read according to its place values.
e.g. 10,024 is read as 'Ten thousand twenty-four'.
Ascending Order
Arranging numbers from the smallest to the largest (increasing order).
e.g. 18,926; 34,407; 34,740; 40,347; 40,473; 47,340; 73,404; 74,430.
Descending Order
Arranging numbers from the largest to the smallest (decreasing order).
e.g. 66,540; 65,232; 56,380; 53,231; 51,336; 45,858.
Comparing Numbers
Determining which number is greater or smaller by comparing digits from the highest place value (Ten Thousands) to the lowest (Ones).
e.g. 49,014 is greater than 9,990 because 49,014 has 4 Ten Thousands (40,000) while 9,990 has 0 Ten Thousands (only 9,990).
Rounding to Nearest Ten
Finding the multiple of 10 that is closest to a given number. If the ones digit is 0-4, round down; if 5-9, round up.
e.g. 2,346 rounded to the nearest ten is 2,350 (since 6 ≥ 5, we round up).
Rounding to Nearest Hundred
Finding the multiple of 100 closest to a given number. Look at the tens digit: 0-4 round down, 5-9 round up.
e.g. 2,346 rounded to the nearest hundred is 2,300 (since tens digit 4 < 5, we round down).
Rounding to Nearest Thousand
Finding the multiple of 1000 closest to a given number. Look at the hundreds digit: 0-4 round down, 5-9 round up.
e.g. 2,346 rounded to the nearest thousand is 2,000 (since hundreds digit 3 < 5, we round down).
Digit Swap
Interchanging two digits in a number to create a new number, often used to explore place value and comparison.
e.g. In 1,478, swapping 7 and 4 gives 1,748.
Token Representation
Using physical tokens (like bundles of 10,000, 1,000, 100, 10, 1) to model the place value of a number.
e.g. 45,867 is shown as 4 tokens of 10,000, 5 tokens of 1,000, 8 tokens of 100, 6 tokens of 10, and 7 tokens of 1.
Neighbouring Tens/Hundreds/Thousands
The two multiples of 10, 100, or 1000 that a number lies between on the number line.
e.g. 2,346 lies between 2,340 and 2,350 (neighbouring tens), between 2,300 and 2,400 (neighbouring hundreds), and between 2,000 and 3,000 (neighbouring thousands).
Formulas & Equations (5)
10 Ones = 1 Ten = 10
Reads as: Ten ones make one ten, which is equal to ten.
Variables: Ones: single units; Ten: group of 10 ones.
Use when: Understanding the base-10 place value system and converting between units.
⚠ Students think 10 ones = 10 tens. Actually 10 ones = 1 ten, not 10 tens.
10 Tens = 1 Hundred = 100
Reads as: Ten tens make one hundred, which is equal to one hundred.
Variables: Tens: group of 10; Hundred: group of 100.
Use when: Converting between tens and hundreds in place value.
⚠ Writing 10 tens = 1000 instead of 100.
10 Hundreds = 1 Thousand = 1,000
Reads as: Ten hundreds make one thousand, which is equal to one thousand.
Variables: Hundreds: group of 100; Thousand: group of 1000.
Use when: Converting hundreds to thousands.
⚠ Confusing 10 hundreds with 10,000 (ten thousands).
10 Thousands = 1 Ten Thousand = 10,000
Reads as: Ten thousands make one ten thousand, which is equal to ten thousand.
Variables: Thousands: group of 1000; Ten Thousand: group of 10,000.
Use when: Extending place value to five-digit numbers.
⚠ Writing 10,000 as 1000 with an extra zero, or misplacing the comma.
1 km = 1,000 m
Reads as: One kilometre is equal to one thousand metres.
Variables: km: kilometre (unit of distance); m: metre.
Use when: Converting between kilometres and metres in travel distance problems.
⚠ Writing 1 km = 100 m instead of 1000 m.
How It Works
Reading and Writing Large Numbers (up to 5 digits)
  1. Step 1: Identify the number of digits. If there are 5 digits, the leftmost digit is in the Ten Thousands place.
  2. Step 2: Write the digits in a place value chart with columns TTh, Th, H, T, O.
  3. Step 3: Read the number from left to right: say the number in the TTh and Th places together as 'X thousand', then the remaining three digits as a normal three-digit number.
  4. Step 4: Insert a comma after the first digit from the left (for 5-digit numbers) to separate the ten thousands and thousands.
  5. Step 5: Write the number name accordingly, e.g., 45,867 is 'Forty-five thousand eight hundred sixty-seven'.
💡 Students often forget to write the comma or misplace it. For 5-digit numbers, the comma goes after the first digit (e.g., 10,000 not 10000).
Comparing Two Large Numbers
  1. Step 1: Count the number of digits. The number with more digits is greater.
  2. Step 2: If both have the same number of digits, compare the digits from the highest place (TTh) to the lowest (O).
  3. Step 3: At the first place where the digits differ, the number with the larger digit is greater.
  4. Step 4: Use a place value chart to align digits if needed.
💡 A common mistake is comparing only the first digit without considering the number of digits. 9,990 is less than 49,014 because 49,014 has 5 digits (ten thousands place) while 9,990 has only 4 digits.
Rounding to the Nearest Ten
  1. Step 1: Look at the ones digit of the number.
  2. Step 2: If the ones digit is 0, 1, 2, 3, or 4, round down to the previous ten (keep the tens digit same, ones become 0).
  3. Step 3: If the ones digit is 5, 6, 7, 8, or 9, round up to the next ten (increase the tens digit by 1, ones become 0).
💡 Students often round based on the tens digit instead of the ones digit. For nearest ten, only the ones digit matters.
Rounding to the Nearest Hundred
  1. Step 1: Look at the tens digit of the number.
  2. Step 2: If the tens digit is 0, 1, 2, 3, or 4, round down to the previous hundred (hundreds digit stays same, tens and ones become 0).
  3. Step 3: If the tens digit is 5, 6, 7, 8, or 9, round up to the next hundred (increase the hundreds digit by 1, tens and ones become 0).
💡 Students sometimes look at the ones digit instead of the tens digit. For nearest hundred, the tens digit is the deciding factor.
Rounding to the Nearest Thousand
  1. Step 1: Look at the hundreds digit of the number.
  2. Step 2: If the hundreds digit is 0, 1, 2, 3, or 4, round down to the previous thousand (thousands digit stays same, hundreds, tens, ones become 0).
  3. Step 3: If the hundreds digit is 5, 6, 7, 8, or 9, round up to the next thousand (increase the thousands digit by 1, hundreds, tens, ones become 0).
💡 For nearest thousand, the hundreds digit is the key. Do not look at the tens or ones.
Writing Numbers in Expanded Form
  1. Step 1: Identify the place value of each digit (TTh, Th, H, T, O).
  2. Step 2: Multiply each digit by its place value (e.g., 4 in TTh = 40,000).
  3. Step 3: Write the sum of these values, separated by plus signs.
  4. Step 4: For zero digits, you can skip them or write +0.
💡 Students often forget to include the place value multiplier. For 10,304, the expanded form is 10,000 + 0 + 300 + 0 + 4, or simply 10,000 + 300 + 4.
Digit Swap to Create Larger or Smaller Numbers
  1. Step 1: Identify the two digits you want to swap.
  2. Step 2: Exchange their positions in the number.
  3. Step 3: Compare the new number with the original to see if it is larger or smaller.
  4. Step 4: To make the largest possible number, swap a smaller digit from a higher place with a larger digit from a lower place.
💡 Swapping digits changes the place value of each digit, so the new number can be very different. Always check the place value chart.
Finding Numbers Between Two Given Numbers
  1. Step 1: Identify the smaller and larger boundary numbers.
  2. Step 2: Any number greater than the smaller and less than the larger is between them.
  3. Step 3: For numbers with zeros in ones, tens, and hundreds, ensure those digits are 0.
  4. Step 4: List numbers in increasing order.
💡 The boundary numbers themselves are not included. For example, numbers between 42,750 and 53,500 with zeros in ones, tens, hundreds: 43,000; 44,000; ... 53,000.
Counting Notes of a Given Denomination in a Number
  1. Step 1: Divide the number by the denomination value (e.g., for ₹10 notes, divide by 10).
  2. Step 2: The quotient gives the number of notes of that denomination.
  3. Step 3: For ₹500 notes, divide by 500. Use the hint: number of thousands × 2 gives number of ₹500 notes (since 2 × 500 = 1000).
💡 For ₹500 notes, do not simply divide by 500 if the number is not a multiple of 500. Use the relationship: 1 thousand = 2 notes of ₹500.
Exam Traps — Don't Make These Mistakes
⚠ Comparing numbers with different digit lengths
✗ 9,990 is greater than 49,014 because 9 is greater than 4.
→ The student compared only the first digit without considering the number of digits. 49,014 has 5 digits (ten thousands place) while 9,990 has only 4 digits. A 5-digit number is always greater than a 4-digit number.
✓ 49,014 is greater than 9,990 because 49,014 has 5 digits (it is in the ten thousands) while 9,990 has only 4 digits (it is in the thousands).
⚠ Misplacing the comma in 5-digit numbers
✗ 10000 (no comma) or 10,0000 (comma after two digits).
→ In the Indian system, for 5-digit numbers, the comma is placed after the first digit from the left (ten thousands place). 10000 without a comma is hard to read; 10,0000 is incorrect because it suggests 1,00,000 (one lakh).
✓ 10,000 (comma after the first digit).
⚠ Rounding to nearest hundred using the ones digit
✗ 2,346 rounded to nearest hundred is 2,400 because 6 ≥ 5.
→ For rounding to the nearest hundred, we look at the tens digit, not the ones digit. The tens digit is 4, which is less than 5, so we round down to 2,300.
✓ 2,346 rounded to the nearest hundred is 2,300 because the tens digit (4) is less than 5.
⚠ Expanded form missing place value multipliers
✗ 8,062 = 8 + 0 + 6 + 2.
→ The student wrote only the digits, not their place values. 8 is in the thousands place, so it should be 8,000; 0 in hundreds; 60 in tens; 2 in ones.
✓ 8,062 = 8,000 + 0 + 60 + 2 (or 8 Thousands + 0 Hundreds + 6 Tens + 2 Ones).
⚠ Confusing 'nearest ten' with 'nearest tens digit'
✗ The nearest ten of 2,346 is 2,340 because 46 is closer to 40 than 50.
→ The student is thinking of the last two digits, but the rule is based on the ones digit. The ones digit is 6, which is ≥ 5, so we round up to 2,350.
✓ 2,346 rounded to the nearest ten is 2,350 because the ones digit (6) is 5 or more, so we round up.
⚠ Incorrectly counting ₹500 notes from a number
✗ Number of ₹500 notes in ₹7,934 is 7,934 ÷ 500 = 15.868, so 15 notes.
→ The division gives a decimal, but the correct method uses the relationship: 1 thousand = 2 notes of ₹500. 7,934 has 7 thousands, so 7 × 2 = 14 notes of ₹500 (since 7,000 = 14 × 500). The remaining 934 is less than 500, so no extra note.
✓ 7,934 has 7 thousands. Since 1 thousand = 2 notes of ₹500, number of ₹500 notes = 7 × 2 = 14.
Compare & Contrast
Which digit is used to decide rounding
Rounding to Nearest Ten
Rounding to Nearest Hundred
For nearest ten, look at the ones digit. For nearest hundred, look at the tens digit.
Direction of arrangement
Ascending Order
Descending Order
Ascending order arranges numbers from smallest to largest (increasing). Descending order arranges from largest to smallest (decreasing).
Exam Focus
Marks pattern: 2 MCQs (1 mark each) on place value or number names, 1 Short Answer (2-3 marks) on expanded form or rounding, 1 Long Answer (4-5 marks) on comparing/ordering or word problems involving large numbers.
Most asked: Reading and writing number names for 5-digit numbers · Expanded form of numbers · Comparing and ordering numbers (ascending/descending) · Rounding to nearest ten, hundred, thousand · Place value chart and identifying digit values
Don't skip: Word problems involving comparison of distances or populations (e.g., whose car has been driven more?); Arranging numbers in ascending or descending order with 5-digit numbers; Rounding a given number to the nearest ten, hundred, and thousand (table format)
One-Line Revision (read aloud before the exam)
  1. 10 Ones = 1 Ten, 10 Tens = 1 Hundred, 10 Hundreds = 1 Thousand, 10 Thousands = 1 Ten Thousand.
  2. A 5-digit number has a Ten Thousands place (TTh), then Thousands (Th), Hundreds (H), Tens (T), and Ones (O).
  3. Use a comma after the first digit from the left in a 5-digit number, e.g., 10,000.
  4. To compare numbers, first check the number of digits; more digits means a larger number.
  5. For rounding to the nearest ten, look at the ones digit: 0-4 round down, 5-9 round up.
  6. For rounding to the nearest hundred, look at the tens digit: 0-4 round down, 5-9 round up.
  7. For rounding to the nearest thousand, look at the hundreds digit: 0-4 round down, 5-9 round up.
  8. Expanded form shows each digit multiplied by its place value, e.g., 8,062 = 8,000 + 60 + 2.
  9. Ascending order means smallest to largest; descending order means largest to smallest.
  10. Number names for 5-digit numbers: say the first two digits as 'X thousand', then the last three as a normal number.
  11. 1 km = 1,000 m.
  12. To find how many ₹500 notes are in a number, multiply the number of thousands by 2.
  13. A digit swap changes the place value of digits, so the new number can be very different from the original.
  14. The caretaker's trick with horses shows that counting along sides double-counts corner horses.

MCQs — 10 Questions with Answers

Q1. What is the place value of 5 in the number 15,347?

  • A. 5,000 (five thousands) ✓
  • B. 500 (five hundreds)
  • C. 50 (five tens)
  • D. 5 (five ones)

Answer: A — The digit 5 is in the Thousands place (Th), so its value is 5 × 1,000 = 5,000.

Q2. Which number is written as 'Thirty-six thousand two hundred fourteen'?

  • A. 36,214 ✓
  • B. 36,024
  • C. 30,614
  • D. 36,124

Answer: A — Thirty-six thousand (36,000) + two hundred (200) + fourteen (14) = 36,214.

Q3. What is 10,000 + 5,000 + 300 + 20 + 4 equal to?

  • A. 10,524
  • B. 15,324 ✓
  • C. 15,234
  • D. 51,234

Answer: B — Adding: 10,000 + 5,000 = 15,000; then + 300 = 15,300; + 20 = 15,320; + 4 = 15,324.

Q4. What is the nearest ten to the number 2,347?

  • A. 2,340
  • B. 2,350 ✓
  • C. 2,300
  • D. 2,400

Answer: B — Since the ones digit is 7 (which is 5 or more), we round up to the next ten: 2,350.

Q5. Which of these numbers has the same nearest hundred as 5,678?

  • A. 5,810
  • B. 5,620
  • C. 5,749 ✓
  • D. 5,550

Answer: C — 5,678 rounds to 5,700 (nearest hundred, since tens digit 7 >= 5). Checking each option: A) 5,810 → 5,800; B) 5,620 → 5,600; C) 5,749 → 5,700 ✓; D) 5,550 → 5,600.

Q6. A cyclist covers 15 km in one hour. How much distance will she cover in 4 hours?

  • A. 45 km
  • B. 50 km
  • C. 55 km
  • D. 60 km ✓

Answer: D — Distance in 4 hours = 15 km × 4 = 60 km.

Q7. A school has 461 girls and 439 boys. How many students in total?

  • A. 890
  • B. 900 ✓
  • C. 800
  • D. 910

Answer: B — Total students = 461 + 439 = 900.

Q8. In the number 48,362, which digit is in the ten thousands place?

  • A. 4 ✓
  • B. 8
  • C. 3
  • D. 6

Answer: A — Reading from left: 4 is in the ten thousands (TTh) place, 8 in thousands, 3 in hundreds, 6 in tens, 2 in ones.

Q9. How many bicycles are needed if 900 students need to travel and each bicycle can hold 2 students?

  • A. 400
  • B. 450 ✓
  • C. 500
  • D. 550

Answer: B — Number of bicycles = 900 ÷ 2 = 450 bicycles.

Q10. What is the nearest thousand to 7,568?

  • A. 7,000
  • B. 8,000 ✓
  • C. 7,500
  • D. 7,600

Answer: B — The hundreds digit is 5, so we round up: 7,568 rounds to 8,000 (nearest thousand).

Flashcards

What does TTh stand for in the place value chart?

TTh stands for Ten Thousand, which is the place to the left of the Thousands place.

How many ones equal one ten?

10 ones equal 1 ten, written as 10.

How do we write the number ten thousand?

We write ten thousand as 10,000 using a comma after the ten thousands digit.

What is 9,000 + 1,000 equal to?

9,000 + 1,000 = 10,000 (ten thousand).

Write the number name for 13,520.

13,520 is read as thirteen thousand five hundred twenty.

What is the nearest ten to 2,346?

The nearest ten to 2,346 is 2,350.

What is the nearest hundred to 2,346?

The nearest hundred to 2,346 is 2,300.

How many thousands are in the number 45,867?

There are 45 thousands in 45,867 (shown by the digits 45 in the TTh and Th places).

When comparing 9,990 and 49,014, which is larger?

49,014 is larger because it has 4 ten thousands while 9,990 has 0 ten thousands.

How do we break down the number 1,380 using place value?

1,380 = 1 Thousand + 3 Hundreds + 8 Tens + 0 Ones.

Important Board Questions

Write the number 'twenty-three thousand four hundred fifty-six' in digits. [1 mark]

Break the number name by places: twenty-three thousand (23,000) + four hundred (400) + fifty-six (56). Use the comma after the ten thousands place.

Fill in the blanks: (a) 10 Hundreds = 1 ______ (b) 10 Thousands = 1 ______ [2 marks]

Think about the place value sequence: Ones → Tens → Hundreds → Thousands → Ten Thousands. Each place is 10 times the previous one.

A school trip has 461 girls and 439 boys. If an autorickshaw can carry 3 people, how many autorickshaws are needed? (Show your working.) [3 marks]

Step 1: Add girls and boys to find total students (461 + 439). Step 2: Divide the total by 3 (capacity per autorickshaw) and round up if there is a remainder.

Compare the numbers 9,990 and 49,014 using a place value chart. Which is larger and why? Draw a place value chart to show your answer. [5 marks]

Create two rows in a place value chart with columns TTh, Th, H, T, O. Compare digit by digit starting from the leftmost (TTh) place. The number with more ten thousands is larger. Explain that position of the digit is more important than the digit value itself.

True or False: The nearest hundred of 3,456 is the same as the nearest hundred of 3,489. Give a reason. [2 marks]

For 3,456: look at the tens digit (5 or more, so round up). For 3,489: look at the tens digit (8, so round up). Check if both round to the same hundred.

Assertion-Reason Questions for Reading and Writing Large Numbers

Q1. Assertion (A):

The number 10,000 is called ten thousand because it has 1 in the ten thousands place.

Reason (R):

The ten thousands place is the fifth place from the right in our number system.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both the assertion and reason are true. The reason correctly explains why we call 10,000 as ten thousand—because of the place value system where the fifth place from right is ten thousands.

Q2. Assertion (A):

49,014 is greater than 9,990.

Reason (R):

Both numbers have the same first digit.

Answer: C — A is true but R is false — The assertion is true (49,014 > 9,990), but the reason is false. They do NOT have the same first digit (4 ≠ 9). We compare by first digit from the left, and 49,014 has a 4 in the ten thousands place while 9,990 only reaches thousands.

Q3. Assertion (A):

10 hundreds equal 1 thousand.

Reason (R):

The thousands place comes after the hundreds place in the place value system.

Answer: B — Both A and R are true, but R is NOT the correct explanation of A — Both the assertion and reason are true. 10 hundreds = 1,000 = 1 thousand. However, the reason does not correctly explain the assertion—it just states the order of places, not the relationship. The assertion is true because of multiplication (10 × 100 = 1,000).

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Case-Based Questions (CBQ) for Reading and Writing Large Numbers

Case Study:

Mina is preparing for a school trip. The school has 461 girls and 439 boys. The teacher asks: 'How many students are going?' Then the teacher says, 'We have minibuses that can take 25 students each. Let's arrange the trip properly.' Mina does the maths: 461 + 439 = 900 students total.

Q1. How many students are going on the trip in total?

  • A. 900 students ✓
  • B. 850 students
  • C. 920 students
  • D. 800 students

Answer: A

Q2. If each minibus takes 25 students, how many minibuses are needed for 900 students?

  • A. 36 minibuses ✓
  • B. 30 minibuses
  • C. 40 minibuses
  • D. 35 minibuses

Answer: A

Q3. Write 900 in words as a number name.

  • A. Nine thousand
  • B. Nine hundred ✓
  • C. Ninety hundred
  • D. Nine hundred thousand

Answer: B

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