Class 4 — Mathematics
Large Numbers
Class 4
- ✓By the end of this lesson students will be able to read and write numbers up to 6 digits.
- ✓By the end of this lesson students will be able to identify the place value and face value of digits in 5-digit and 6-digit numbers.
- ✓By the end of this lesson students will be able to write numbers in expanded form.
- ✓By the end of this lesson students will be able to compare and order large numbers.
- ✓By the end of this lesson students will be able to round numbers to the nearest 10, 100, and 1000.
Key concepts
We know that the greatest 4-digit number is 9999. When we add 1 to 9999, we get 10000, which is the smallest 5-digit number. It is read as Ten Thousand. Similarly, the greatest 5-digit number is 99999. When we add 1 to 99999, we get 100000, which is the smallest 6-digit number. It is read as One Lakh. We use the Indian Place Value System to read and write these numbers. The places are Ones, Tens, Hundreds, Thousands, Ten Thousands, and Lakhs. Commas are used to separate periods: the first comma comes after the Hundreds place, and then after every two digits.
The 'place value' of a digit is its value based on its position in the number. For example, in 456789, the place value of 5 is 5 Ten Thousands or 50,000. The 'face value' of a digit is the digit itself, regardless of its position. For example, in 456789, the face value of 5 is simply 5.
Writing a number in its expanded form means expressing it as the sum of the place values of its digits. For example, the number 4,56,789 can be written in expanded form as: 4,00,000 + 50,000 + 6,000 + 700 + 80 + 9.
To compare numbers, first count the number of digits. The number with more digits is always greater. If the number of digits is the same, compare the digits from the leftmost place until you find a difference. The number with the greater digit at that position is the greater number. Ordering numbers means arranging them in 'ascending order' (smallest to greatest) or 'descending order' (greatest to smallest).
Rounding a number means approximating it to the nearest 10, 100, or 1000. \n1. To round to the nearest 10: Look at the digit in the ones place. If it is 5 or more (5, 6, 7, 8, 9), round up the tens digit and change the ones digit to 0. If it is less than 5 (0, 1, 2, 3, 4), keep the tens digit as it is and change the ones digit to 0.\n2. To round to the nearest 100: Look at the digit in the tens place. If the number formed by the tens and ones digits is 50 or more, round up the hundreds digit and change the tens and ones digits to 00. If it is less than 50, keep the hundreds digit as it is and change the tens and ones digits to 00.\n3. To round to the nearest 1000: Look at the digit in the hundreds place. If the number formed by the hundreds, tens, and ones digits is 500 or more, round up the thousands digit and change the hundreds, tens, and ones digits to 000. If it is less than 500, keep the thousands digit as it is and change the hundreds, tens, and ones digits to 000.
Key facts to remember
- 1The smallest 5-digit number is 10,000 (Ten Thousand).
- 2The greatest 5-digit number is 99,999 (Ninety-nine thousand nine hundred ninety-nine).
- 3The smallest 6-digit number is 1,00,000 (One Lakh).
- 4The greatest 6-digit number is 9,99,999 (Nine lakh ninety-nine thousand nine hundred ninety-nine).
- 5Place value is the value of a digit based on its position, while face value is the digit itself.
- 6In the Indian Place Value System, commas are placed after the hundreds place, then after every two digits (e.g., 4,56,789).
- 7When rounding, if the digit to the right of the rounding place is 5 or more, round up. Otherwise, round down.
Worked examples
Example 1
Write the number name for 456789 and find the place value of the digit 5.
Answer
Number name: Four lakh fifty-six thousand seven hundred eighty-nine. The place value of the digit 5 is 50,000.
Example 2
Write 70345 in expanded form. Also, form the greatest and smallest 5-digit numbers using the digits 2, 0, 8, 1, 5.
Answer
Expanded form of 70345 is 70000 + 0 + 300 + 40 + 5. The greatest 5-digit number is 85210. The smallest 5-digit number is 10258.
Remember that a number cannot begin with the digit 0.
Example 3
Round the number 34567 to the nearest 10, nearest 100, and nearest 1000.
Answer
34567 rounded to the nearest 10 is 34570. 34567 rounded to the nearest 100 is 34600. 34567 rounded to the nearest 1000 is 35000.
Common mistakes
- ✗Confusing the Indian Place Value System with the International Place Value System (e.g., writing 456,789 instead of 4,56,789).
- ✗Incorrectly identifying place values, especially when zeros are present in the number.
- ✗Starting the smallest number with zero when forming numbers from given digits (e.g., writing 01258 instead of 10258).
- ✗Incorrectly applying rounding rules, particularly when the digit to be considered is exactly 5 (e.g., rounding 35 to 30 instead of 40).
- ✗Forgetting to change all digits to the right of the rounding place to zero after rounding.
Exam tips
- ★Always read the question carefully to understand what is being asked (e.g., place value vs. face value, nearest 10 vs. nearest 100).
- ★Use the Indian Place Value Chart to correctly identify the place of each digit, especially for large numbers.
- ★When rounding, underline the digit in the place you are rounding to, and circle the digit to its right. This helps in applying the rule correctly.
- ★Practice writing numbers in both standard and expanded forms to strengthen your understanding of place value.
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