1. What is Place Value?
Place value refers to the value of a digit based on its position in a number. In a number, the value of each digit depends on its position from right to left. The places follow a pattern based on powers of 10.
Place Value Chart (For a large number like 1,234,567):
| Place | Value | Example in 1,234,567 |
|---|---|---|
| Millions | 10610^6106 (1,000,000) | 1,000,000 |
| Hundred Thousands | 10510^5105 (100,000) | 200,000 |
| Ten Thousands | 10410^4104 (10,000) | 30,000 |
| Thousands | 10310^3103 (1,000) | 4,000 |
| Hundreds | 10210^2102 (100) | 500 |
| Tens | 10110^1101 (10) | 60 |
| Ones (Units) | 10010^0100 (1) | 7 |
2. How to Read and Write Numbers Using Place Value
When reading large numbers, divide them into groups of three digits, called periods. Each period is read separately.
Example 1:
Number: 56,321
How to read it: Fifty-six thousand, three hundred twenty-one.
Example 2:
Number: 2,103,567
How to read it: Two million, one hundred three thousand, five hundred sixty-seven.
Activity:
Write these numbers in words:
- 450,789
- 3,067,251
- 72,408
3. Identifying Place Value of a Digit
To find the place value of a digit, locate its position in the number.
Example 1:
In the number 6,372:
- The place value of 6 is 6,000 (thousands place).
- The place value of 3 is 300 (hundreds place).
- The place value of 7 is 70 (tens place).
- The place value of 2 is 2 (ones place).
Example 2:
In the number 97,624:
- The place value of 9 is 90,000 (ten-thousands place).
- The place value of 7 is 7,000 (thousands place).
Activity:
Find the place value of the underlined digit:
- 12,567
- 64,823
- 715,239
4. Expanded Form of Numbers
The expanded form breaks down a number based on the place value of each digit.
Example 1:
Number: 5,432
Expanded form:
5,432=5,000+400+30+25,432 = 5,000 + 400 + 30 + 25,432=5,000+400+30+2
Example 2:
Number: 68,259
Expanded form:
68,259=60,000+8,000+200+50+968,259 = 60,000 + 8,000 + 200 + 50 + 968,259=60,000+8,000+200+50+9
Activity:
Write the expanded form of these numbers:
- 9,326
- 24,501
- 103,457
5. Comparing Numbers Using Place Value
To compare two numbers, start by looking at the digit in the highest place value. The larger digit in the highest place indicates the larger number. If the digits are the same, compare the next place value.
Example 1:
Compare 45,327 and 46,298:
- The digits in the ten-thousands place are the same (4).
- In the thousands place, 6 > 5, so 46,298 > 45,327.
Example 2:
Compare 78,230 and 78,129:
- The digits in the ten-thousands and thousands places are the same.
- In the hundreds place, 2 > 1, so 78,230 > 78,129.
Activity:
Compare the following numbers:
- 93,451 and 94,510
- 58,607 and 58,706
- 7,923 and 7,932
6. Rounding Numbers Using Place Value
When rounding numbers, use the digit to the right of the place value you are rounding to:
- If the digit is 5 or more, round up.
- If the digit is less than 5, round down.
Example 1: Rounding to the nearest ten
Number: 562
- The digit in the tens place is 6.
- The next digit is 2 (which is less than 5), so we round down.
Rounded number: 560
Example 2: Rounding to the nearest thousand
Number: 3,462
- The digit in the thousands place is 3.
- The next digit is 4 (which is less than 5), so we round down.
Rounded number: 3,000
Activity:
Round the following numbers:
- 7,532 to the nearest hundred.
- 25,781 to the nearest thousand.
- 123,487 to the nearest ten thousand.
7. More Examples
7.1: Large Number Identification
Question:
The population of a city is 456,782. Write the population in words.
Solution:
Four hundred fifty-six thousand, seven hundred eighty-two.
7.2: Place Value Understanding
Question:
In the number 92,467, what is the value of the digit 9?
Solution:
The value of the digit 9 is 90,000 because it is in the ten-thousands place.
7.3: Expanded Form
Question:
Write 73,561 in expanded form.
Solution:
73,561=70,000+3,000+500+60+173,561 = 70,000 + 3,000 + 500 + 60 + 173,561=70,000+3,000+500+60+1
7.4: Comparing Numbers
Question:
Which is greater, 67,284 or 68,173?
Solution:
Compare the ten-thousands place:
- 6 = 6
- In the thousands place, 8 > 7. Therefore, 68,173 > 67,284.
7.5: Rounding Numbers
Question:
Round 74,592 to the nearest hundred.
Solution:
- The digit in the hundreds place is 5.
- The next digit is 9, so we round up.
Rounded number: 74,600
8. Expanded Form Using Place Value
Expanded form shows the value of each digit based on its place value. It is a way to decompose a number to see the value of each individual digit.
Example 1: Expanded Form
Number: 7,385
- The digit 7 is in the thousands place, so it represents 7,000.
- The digit 3 is in the hundreds place, so it represents 300.
- The digit 8 is in the tens place, so it represents 80.
- The digit 5 is in the ones place, so it represents 5.
Expanded Form: 7,000 + 300 + 80 + 5
Example 2: Expanded Form of a Large Number
Number: 2,456,891
- The digit 2 is in the millions place, so it represents 2,000,000.
- The digit 4 is in the hundred thousands place, so it represents 400,000.
- The digit 5 is in the ten thousands place, so it represents 50,000.
- The digit 6 is in the thousands place, so it represents 6,000.
- The digit 8 is in the hundreds place, so it represents 800.
- The digit 9 is in the tens place, so it represents 90.
- The digit 1 is in the ones place, so it represents 1.
Expanded Form: 2,000,000 + 400,000 + 50,000 + 6,000 + 800 + 90 + 1
9. Practice Problems
- Write 89,321 in words.
- Find the place value of 6 in the number 164,903.
- Compare 45,892 and 45,918. Which is larger?
- Write the expanded form of 29,457.
- Round 53,789 to the nearest thousand.
| << Previous: Numbers Basic Concepts | Next: Compare Numbers >> |
Practice makes perfect. We recommend you to practice topic-wise tests https://rankmadeeasy.com/courses-and-test-series . Our expert team has prepared these tests to help you become confident in each topic.
Our Social Media Presence –
https://youtube.com/@rankmadeeasy
https://www.facebook.com/groups/rankmadeeasy
https://www.facebook.com/RankMadeEasy
https://www.instagram.com/rankmadeeasy
https://x.com/rankmadeeasy
https://linkedin.com/in/rankmadeeasy