Examples:

• 4,582,301 = "Four million, five hundred eighty-two thousand, three hundred one"
• 7,000,429 = "Seven million, four hundred twenty-nine"
• 1,234,567 = "One million, two hundred thirty-four thousand, five hundred sixty-seven"

Writing Numbers in Different Forms

Standard form: 3,456,789 Word form: Three million, four hundred fifty-six thousand, seven hundred eighty-nine Expanded form: 3,000,000 + 400,000 + 50,000 + 6,000 + 700 + 80 + 9

Comparing Large Numbers

Strategy:

1. Compare digit by digit from LEFT to RIGHT
2. The first digit that's different tells you which is bigger

Example: Which is bigger: 3,456,789 or 3,492,103?

• Same millions digit (3)
• Same hundred thousands (4)
• Different ten thousands: 5 vs 9
• 9 > 5, so 3,492,103 is bigger ✓

Value vs Digit

Important distinction:

• The digit is the number itself (like 5)
• The value is what it represents based on position

In 5,234,678:

• The digit 5 has a VALUE of 5,000,000 (five million)
• The digit 2 has a VALUE of 200,000 (two hundred thousand)
• The digit 3 has a VALUE of 30,000 (thirty thousand)

Powers of 10

Understanding place value helps with multiplying by 10, 100, 1,000:

Multiply by 10: Move each digit one place LEFT (add a zero)

• 345 × 10 = 3,450

Multiply by 100: Move each digit two places LEFT

• 345 × 100 = 34,500

Multiply by 1,000: Move each digit three places LEFT

• 345 × 1,000 = 345,000

Real-World Examples

Population:

• New York City: about 8,000,000 people (8 million)

Money:

• A millionaire has: $1,000,000 or more

Distance:

• Distance to the moon: about 240,000 miles

Big numbers in nature:

• Grains of sand on a beach: millions!
• Stars in the sky: billions!

Practice Tips

To remember place values:

1. Use commas to separate periods (every 3 digits)
2. Practice saying numbers out loud
3. Write numbers in different forms
4. Use a place value chart

Common patterns:

• 1,000 = 1 thousand
• 10,000 = 10 thousand
• 100,000 = 100 thousand
• 1,000,000 = 1 million

Common Mistakes

❌ Forgetting commas when writing large numbers ❌ Saying "and" when reading whole numbers ❌ Mixing up the order of periods

✅ Use commas every 3 digits from the right ✅ Read each period separately, then say its name ✅ Remember the order: ones, thousands, millions

Write the number: 3 millions, 5 hundred thousands, 2 tens, 9 ones