Place Value and Rounding Numbers
Table Of Contents
🎬 Math Angel Video: Understanding Place Value
What is a Place Value Chart?
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A place value chart helps you understand the value of each digit in a number based on its position.
Each digit sits in a column with a special name, and that name tells you how much the digit is worth.
Example: Place Value Chart of 54,321
| Place | Ten Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|
| Digit | 5 | 4 | 3 | 2 | 1 |
| Place Value | 5 ten-thousands = 50,000 | 4 thousands = 4,000 | 3 hundreds = 300 | 2 tens = 20 | 1 |
🛎️ What Each Digit Means:
- The 5 in Ten Thousands is worth 50,000
- The 4 in Thousands is worth 4,000
- The 3 in Hundreds is worth 300
- The 2 in Tens is worth 20
- The 1 in Ones is worth 1
Adding them together: 50,000 + 4,000 + 300 + 20 + 1 = 54,321
🛎️ How to Read a Number?
We read the number from left to right. For example, you pronounce 54,321 as “Fifty-four thousand, three hundred twenty-one.”
What Is the Base-10 System?
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The Base-10 system (also called the decimal system) is the number system we use every day.
It’s called “base 10” because it’s built on 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
🛎️ Place Value in the Base-10 System Explained
In the Base-10 system, each place to the left is worth 10 times more than the place on the right.
For example, as shown below, the digit 2 is worth more and more as it moves to the left.
| Place | Place Value |
|---|---|
| Ones | 2 |
| Tens | 20 |
| Hundreds | 200 |
| Thousands | 2,000 |
| Ten Thousands | 20,000 |
Rounding Rules and Steps
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To round a number, follow these steps:
Find the target place value (e.g. tens, hundreds, thousands, millions).
Look at the digit immediately to the right of the target place.
Apply the rounding rule:
If the digit is 0, 1, 2, 3, or 4 → round down (keep the target digit the same).
If the digit is 5, 6, 7, 8, or 9 → round up (increase the target digit by 1).
Replace all digits after the target place with zeros.
How to Round a Number Down (Example)
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🛎️ Example 1: Round 50,245,798 to the nearest million
The target place is the Millions place, and the digit is 0
The digit right after it is 2
Since 2 is less than 5, we round down. That means:
Keep the 0 in the Millions place
Change all digits after it to 0
- Final answer: 50,245,798 rounded to the nearest million is 50,000,000
How to Round a Number Up (Example)
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🛎️ Example: Round 50,245,798 to the nearest thousand
The target place is the Thousands place, and the digit is 5
The digit right after it is 7
Since 7 is greater than 5, we round up. That means:
Increase the 5 in the Thousands place to 6
Change all digits after it to 0
- Final answer: 50,245,798 rounded to the nearest hundred thousand is 50,246,000
📂 Flashcards: Place Value Chart and How to Round Numbers
🍪 Quiz: Practice Place Value and Rounding
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