Place Value with Large Numbers

Understand place value up to millions and write numbers in different forms

Place Value with Large Numbers

Understanding Place Value

Each digit in a number has a value based on its position:

Example: 3,456,789

| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones | |----------|------------------|---------------|-----------|----------|------|------| | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

This number is: 3 million, 456 thousand, 789

Three Forms of Writing Numbers

1. Standard Form

The regular way we write numbers: 3,456,789

2. Word Form

Writing the number in words: three million, four hundred fifty-six thousand, seven hundred eighty-nine

3. Expanded Form

Showing the value of each digit: $3,000,000 + 400,000 + 50,000 + 6,000 + 700 + 80 + 9$

Comparing Large Numbers

Compare digits from left to right:

5,234,567 vs 5,198,432
Same millions place (5)
Compare hundred thousands: 2 > 1
So 5,234,567 > 5,198,432

📚 Practice Problems

1Problem 1easy

❓ Question:

What is the value of the digit 6 in 2,684,301?

💡 Show Solution

Solution:

Look at the place value chart:

The 6 is in the hundred thousands place

Value: $6 \times 100,000 = 600,000$

Answer: 600,000 (six hundred thousand)

2Problem 2medium

❓ Question:

Write 4,507,032 in expanded form.

💡 Show Solution

Solution:

Break down each digit by its place value:

$4,000,000 + 500,000 + 0 + 7,000 + 0 + 30 + 2$

Or simply: $4,000,000 + 500,000 + 7,000 + 30 + 2$

Answer: $4,000,000 + 500,000 + 7,000 + 30 + 2$

3Problem 3hard

❓ Question:

Which number is greater: 8,456,210 or 8,462,105?

💡 Show Solution

Solution:

Compare digit by digit from left to right:

Millions: 8 = 8 ✓
Hundred thousands: 4 = 4 ✓
Ten thousands: 5 < 6 ← Different!

Since $5 < 6$ in the ten thousands place:

Answer: 8,462,105 is greater

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