🔢 Place Values - Grade 3
What is Place Value?
Place value is the value of a digit based on its position in a number!
The same digit can have different values depending on where it sits in the number.
Example: In \(555\), each \(5\) has a different value:
\(500 + 50 + 5\)
đź“Š Place Value Models Up to Hundreds
Place Value Chart (Up to Hundreds)
\(347 = 300 + 40 + 7\)
Place Value Names (Up to Hundreds)
- 🔵 Ones Place: Value = \(1, 2, 3, 4, 5, 6, 7, 8, 9\)
- 🔵 Tens Place: Value = \(10, 20, 30, 40, 50, 60, 70, 80, 90\)
- 🔵 Hundreds Place: Value = \(100, 200, 300, 400, 500, 600, 700, 800, 900\)
Key Formula:
\(\text{Value of a Digit} = \text{Digit} \times \text{Place Value}\)
Example: In \(347\):
• The digit \(3\) is in the hundreds place → \(3 \times 100 = 300\)
• The digit \(4\) is in the tens place → \(4 \times 10 = 40\)
• The digit \(7\) is in the ones place → \(7 \times 1 = 7\)
đź“Š Place Value Names Up to Thousands
Place Value Chart (Up to Thousands)
\(5,347 = 5000 + 300 + 40 + 7\)
Place Value Names (Up to Thousands)
- đź”´ Ones Place: \(1 \times 1 = 1, 2, 3, 4, 5, 6, 7, 8, 9\)
- 🔵 Tens Place: \(\text{digit} \times 10 = 10, 20, 30...\)
- 🟢 Hundreds Place: \(\text{digit} \times 100 = 100, 200, 300...\)
- 🟡 Thousands Place: \(\text{digit} \times 1000 = 1000, 2000, 3000...\)
Important Rules:
- Each place is 10 times greater than the place to its right
- Each place is 10 times smaller than the place to its left
- The value of \(0\) in any place is always \(0\)
đź’Ž Value of a Digit
Two Types of Values
1. Face Value
Face value is the actual digit itself, no matter where it is in the number.
Example: In \(3,456\), the face value of \(4\) is simply \(4\).
2. Place Value
Place value is the value of the digit based on its position.
Example: In \(3,456\), the place value of \(4\) is \(400\) (because it's in the hundreds place).
Formula to Find Value of a Digit
\(\text{Place Value} = \text{Face Value} \times \text{Position Value}\)
Complete Example:
Find the value of each digit in \(7,238\):
Digit 7:
• Position: Thousands place
• Face value: \(7\)
• Place value: \(7 \times 1000 = 7000\)
Digit 2:
• Position: Hundreds place
• Face value: \(2\)
• Place value: \(2 \times 100 = 200\)
Digit 3:
• Position: Tens place
• Face value: \(3\)
• Place value: \(3 \times 10 = 30\)
Digit 8:
• Position: Ones place
• Face value: \(8\)
• Place value: \(8 \times 1 = 8\)
đź“ť Standard and Expanded Form
Three Forms of Numbers
1. Standard Form (Normal Form)
The way we normally write numbers using digits.
Example: \(3,456\)
2. Expanded Form
Shows the value of each digit added together.
Example: \(3,000 + 400 + 50 + 6\)
3. Word Form
The number written in words.
Example: Three Thousand Four Hundred Fifty-Six
Converting Between Forms
Standard → Expanded Form
Steps:
- Identify the place value of each digit
- Multiply each digit by its place value
- Write as addition with + signs
Example: \(5,347\)
\(= 5 \times 1000 + 3 \times 100 + 4 \times 10 + 7 \times 1\)
\(= 5,000 + 300 + 40 + 7\)
Expanded → Standard Form
Steps:
- Add all the values together
- Write the total as one number
Example: \(6,000 + 200 + 30 + 5\)
\(= 6,235\)
Expanded Notation (Alternative Form)
Shows multiplication explicitly:
\(3,456 = (3 \times 1000) + (4 \times 100) + (5 \times 10) + (6 \times 1)\)
🔄 Convert Between Place Values
Understanding Place Value Relationships
\(1\) thousand \(= 10\) hundreds \(= 100\) tens \(= 1000\) ones
Conversion Formulas
Ones ↔ Tens
• \(1\) ten \(= 10\) ones
• \(10\) ones \(= 1\) ten
Example: \(5\) tens \(= 5 \times 10 = 50\) ones
Tens ↔ Hundreds
• \(1\) hundred \(= 10\) tens
• \(10\) tens \(= 1\) hundred
Example: \(3\) hundreds \(= 3 \times 10 = 30\) tens
Hundreds ↔ Thousands
• \(1\) thousand \(= 10\) hundreds
• \(10\) hundreds \(= 1\) thousand
Example: \(7\) thousands \(= 7 \times 10 = 70\) hundreds
Complete Conversion Example
Question: How many tens are in \(3,456\)?
Step 1: Break down the number:
\(3,456 = 3,000 + 400 + 50 + 6\)
Step 2: Convert each part to tens:
• \(3,000 = 300\) tens
• \(400 = 40\) tens
• \(50 = 5\) tens
• \(6 = 0\) tens (with \(6\) ones left over)
Step 3: Add them up:
\(300 + 40 + 5 = 345\) tens
Answer: There are \(345\) tens in \(3,456\) âś“
đź“– Place Value Word Problems
Types of Place Value Problems
Problem Type 1: Finding the Value of a Digit
Problem: In the number \(5,632\), what is the value of the digit \(6\)?
Solution:
Step 1: Identify the position of \(6\) → Hundreds place
Step 2: Multiply by place value → \(6 \times 100 = 600\)
Answer: The value of \(6\) is \(600\) âś“
Problem Type 2: Building Numbers
Problem: What number has \(4\) thousands, \(3\) hundreds, \(0\) tens, and \(7\) ones?
Solution:
Step 1: Write each place value:
• \(4\) thousands = \(4,000\)
• \(3\) hundreds = \(300\)
• \(0\) tens = \(0\)
• \(7\) ones = \(7\)
Step 2: Combine them:
\(4,000 + 300 + 0 + 7 = 4,307\)
Answer: The number is \(4,307\) âś“
Problem Type 3: Comparing Place Values
Problem: How much greater is the value of \(7\) in \(7,234\) than the value of \(7\) in \(4,567\)?
Solution:
Step 1: Find value in first number:
\(7\) in \(7,234\) → Thousands place → \(7,000\)
Step 2: Find value in second number:
\(7\) in \(4,567\) → Ones place → \(7\)
Step 3: Find the difference:
\(7,000 - 7 = 6,993\)
Answer: \(6,993\) times greater âś“
Problem Type 4: Missing Digits
Problem: In the number \(3,?45\), the digit in the hundreds place is \(8\). What is the complete number?
Solution:
Step 1: Identify the missing place → Hundreds
Step 2: Fill in the digit → \(8\)
Answer: The number is \(3,845\) âś“
Steps to Solve Place Value Word Problems
- Read the problem carefully
- Identify what is being asked
- Find the relevant digits and their positions
- Use place value rules and formulas
- Calculate the answer
- Check if your answer makes sense
- Write your answer clearly with units
đź“ť Important Formulas Summary
Main Place Value Formula:
\(\text{Value of Digit} = \text{Face Value} \times \text{Position Value}\)
Place Value Positions:
Ones place: \(\text{digit} \times 1\)
Tens place: \(\text{digit} \times 10\)
Hundreds place: \(\text{digit} \times 100\)
Thousands place: \(\text{digit} \times 1000\)
Expanded Form Formula:
\(\text{Number} = (\text{thousands} \times 1000) + (\text{hundreds} \times 100)\)
\(+ (\text{tens} \times 10) + (\text{ones} \times 1)\)
Conversion Formulas:
\(1\) thousand \(= 10\) hundreds
\(1\) hundred \(= 10\) tens
\(1\) ten \(= 10\) ones
\(1\) thousand \(= 100\) tens
\(1\) thousand \(= 1000\) ones
\(1\) hundred \(= 100\) ones
Relationship Rule:
Each place value is \(10\) times the place to its right
OR
Each place value is \(\frac{1}{10}\) of the place to its left
đź“Š Quick Reference Table
đź’ˇ Quick Learning Tips
- âś“ Remember: The position of a digit determines its value!
- âś“ Each place is 10 times bigger than the one to its right
- âś“ Face value is the digit itself; place value is its worth
- âś“ Use place value charts to organize your thinking
- âś“ In expanded form, always write from largest to smallest
- âś“ When zeros appear, they hold the place but add no value
- âś“ Practice converting between all three forms daily
- âś“ Check your expanded form by adding it back together
- âś“ 10 ones = 1 ten, 10 tens = 1 hundred, 10 hundreds = 1 thousand
- âś“ Read numbers from left to right, starting with the biggest place
- âś“ Use commas to separate thousands from hundreds
- âś“ Always double-check your place value positions!