Whole Numbers and Place Value
Grade 5 Math - Complete Reference Guide
1. Standard and Expanded Form
Key Definitions:
- Standard Form: The normal way of writing numbers (e.g., 4,367)
- Expanded Form: Writing a number as the sum of the value of each digit (e.g., 4,000 + 300 + 60 + 7)
Formula:
Expanded Form = (Digit × Place Value) + (Digit × Place Value) + ...
Examples:
| Standard Form | Expanded Form |
|---|---|
| 589 | 500 + 80 + 9 |
| 9,677 | 9,000 + 600 + 70 + 7 |
| 45,823 | 40,000 + 5,000 + 800 + 20 + 3 |
| 305,042 | 300,000 + 5,000 + 40 + 2 |
Note: Zeros are not written in expanded form!
2. Place Value
Place Value Chart:
| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|---|
| 1,000,000 | 100,000 | 10,000 | 1,000 | 100 | 10 | 1 |
Example: Number 3,465,829
| Digit | Place Value Position | Value |
|---|---|---|
| 3 | Millions | 3,000,000 |
| 4 | Hundred Thousands | 400,000 |
| 6 | Ten Thousands | 60,000 |
| 5 | Thousands | 5,000 |
| 8 | Hundreds | 800 |
| 2 | Tens | 20 |
| 9 | Ones | 9 |
Quick Tips:
- The position of a digit determines its value
- Reading from right to left: ones, tens, hundreds, thousands...
- Use commas every three digits from the right
3. Relationship Between Place Values
Key Rules:
✓ Moving LEFT → Value becomes 10 times LARGER
✓ Moving RIGHT → Value becomes 10 times SMALLER (1/10)
Formulas:
• Next larger place value = Current place value × 10
• Next smaller place value = Current place value ÷ 10
Examples:
| Comparison | Relationship |
|---|---|
| Tens to Ones | 10 ones = 1 ten (10 is 10× larger than 1) |
| Hundreds to Tens | 10 tens = 1 hundred (100 is 10× larger than 10) |
| Thousands to Hundreds | 10 hundreds = 1 thousand (1,000 is 10× larger than 100) |
| Hundreds to Thousands | 100 is 1/10 of 1,000 (100 is 10× smaller than 1,000) |
Example: In 5,523, the 5 in thousands place (5,000) is 10 times larger than the 5 in hundreds place (500).
4. Write Numbers in Words
Rules for Writing Numbers in Words:
- Start from the left (largest place value)
- Use "and" only for decimal points (not for whole numbers)
- Use hyphens for numbers 21-99 (e.g., twenty-one, forty-seven)
- Group numbers by periods: ones, thousands, millions
Examples:
| Number | Words |
|---|---|
| 47 | Forty-seven |
| 538 | Five hundred thirty-eight |
| 4,205 | Four thousand, two hundred five |
| 56,789 | Fifty-six thousand, seven hundred eighty-nine |
| 305,042 | Three hundred five thousand, forty-two |
5. Spell Word Names (Up to 1 Million)
Number Periods:
| Period Name | Place Values | Example |
|---|---|---|
| Ones Period | Ones, Tens, Hundreds | ___,___,456 |
| Thousands Period | Thousands, Ten Thousands, Hundred Thousands | ___,789,___ |
| Millions Period | Millions, Ten Millions, Hundred Millions | 123,___,___ |
Large Number Examples:
| Number | Word Form |
|---|---|
| 10,000 | Ten thousand |
| 75,000 | Seventy-five thousand |
| 123,456 | One hundred twenty-three thousand, four hundred fifty-six |
| 500,000 | Five hundred thousand |
| 1,000,000 | One million |
| 847,592 | Eight hundred forty-seven thousand, five hundred ninety-two |
Tip: Always use commas to separate periods when writing in words!
6. Roman Numerals (I, V, X, L, C, D, M)
Basic Roman Numeral Symbols:
| Roman Numeral | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1,000 |
Rules for Writing Roman Numerals:
Rule 1: When a symbol is repeated, add its value (max 3 times)
Example: III = 3, XX = 20, CCC = 300
Rule 2: When a smaller symbol appears before a larger one, subtract
Example: IV = 4, IX = 9, XL = 40, XC = 90, CD = 400, CM = 900
Rule 3: When a smaller symbol appears after a larger one, add
Example: VI = 6, XI = 11, LX = 60, CX = 110
Rule 4: V, L, and D are never repeated
Common Roman Numeral Examples:
| Number | Roman Numeral | Breakdown |
|---|---|---|
| 4 | IV | 5 - 1 = 4 |
| 9 | IX | 10 - 1 = 9 |
| 14 | XIV | 10 + (5 - 1) = 14 |
| 27 | XXVII | 10 + 10 + 5 + 1 + 1 = 27 |
| 44 | XLIV | (50 - 10) + (5 - 1) = 44 |
| 99 | XCIX | (100 - 10) + (10 - 1) = 99 |
| 500 | D | 500 |
| 1,994 | MCMXCIV | 1000 + (1000-100) + (100-10) + (5-1) |
Quick Reference Summary
Standard ↔ Expanded
Break down by place value
Place Value
Position = Value
Relationships
×10 left, ÷10 right
Number to Words
Use hyphens & commas
Large Numbers
Group by periods
Roman Numerals
I, V, X, L, C, D, M