Place Value

In our number system, the position of a digit tells us its value.

The Decimal System

We use a base-10 (decimal) system. Each place is worth 10 times the place to its right.

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: 5,847

Digit	Place	Value
5	Thousands	5,000
8	Hundreds	800
4	Tens	40
7	Ones	7

Total: $5,000 + 800 + 40 + 7 = 5,847$

Expanded Form

Writing a number as the sum of its place values:

$3,256 = 3,000 + 200 + 50 + 6$

Comparing Numbers

To compare multi-digit numbers:

1. Line up the digits by place value
2. Compare from left to right
3. The first different digit determines which is greater

Example: Compare 4,532 and 4,589

• Thousands: Both have 4 ✓
• Hundreds: Both have 5 ✓
• Tens: 3 vs 8 → 8 is greater

So $4,532 < 4,589$

Rounding

To round to a place value:

1. Look at the digit to the right
2. If it's 5 or greater, round up
3. If it's less than 5, round down

Example: Round 847 to the nearest hundred

• The tens digit is 4 (less than 5)
• Round down: 800