Place Value & Rounding
What You’ll Learn
Section titled “What You’ll Learn”In this lesson you’ll learn how place value organizes numbers, how to read and write large numbers, and how to round numbers to the nearest 10, 100, or 1000. This helps with quick mental math and real-life estimates.
The Concept
Section titled “The Concept”Place value tells us what each digit in a number means based on its position. From right to left:
- Ones place
- Tens place
- Hundreds place
- Thousands place, and so on
Example: In 4,728:
- 4 is in the thousands place ()
- 7 is in the hundreds place ()
- 2 is in the tens place ()
- 8 is in the ones place ()
Total:
Rounding simplifies numbers for estimates. Look at the digit to the right of the place you’re rounding to:
- If it’s 5 or higher, round up.
- If it’s less than 5, round down.
Examples:
- Round 4728 to nearest hundred: Look at tens digit (2 < 5) → 4700
- Round 4728 to nearest thousand: Look at hundreds digit (7 ≥ 5) → 5000
Worked Examples
Section titled “Worked Examples”Round 3,649 to the nearest hundred, then to the nearest thousand.
-
Nearest hundred: Look at tens digit (4 < 5) → round down → 3,600
-
Nearest thousand: Look at hundreds digit (6 ≥ 5) → round up → 4,000
Check: 3,649 is between 3,600 and 3,700 (closer to 3,600), and between 3,000 and 4,000 (closer to 4,000 after rounding up on 6).
Real-World Applications
Section titled “Real-World Applications”Place value helps read prices, bills, or salaries accurately (e.g., 3.80 a gallon” (rounding 500 for groceries this month” (rounding $487), or “The population is roughly 320,000” (rounding 318,742). These shortcuts save time in budgeting, shopping, or planning.