Order of Operations

Whole Numbers and Place Value

By the end of this lesson, you will be able to read and write whole numbers in standard, expanded, and word form, compare and order whole numbers, and apply place value understanding to round numbers.

The Place Value System

Our number system is base-10 (decimal): each position is worth 10 times the position to its right.

Billions	Hundred Millions	Ten Millions	Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
1,000,000,000	100,000,000	10,000,000	1,000,000	100,000	10,000	1,000	100	10	1

Example: 4,382,107

• 4 is in the millions place: $4 \times 1{,}000{,}000 = 4{,}000{,}000$
• 3 is in the hundred thousands place: $3 \times 100{,}000 = 300{,}000$
• 8 is in the ten thousands place: $8 \times 10{,}000 = 80{,}000$
• 2 is in the thousands place: $2 \times 1{,}000 = 2{,}000$
• 1 is in the hundreds place: $1 \times 100 = 100$
• 0 is in the tens place: $0 \times 10 = 0$
• 7 is in the ones place: $7 \times 1 = 7$

Standard, Expanded, and Word Form

Standard form: 4,382,107

Expanded form: $4{,}000{,}000 + 300{,}000 + 80{,}000 + 2{,}000 + 100 + 0 + 7$

Word form: four million, three hundred eighty-two thousand, one hundred seven

Comparing and Ordering Whole Numbers

To compare, line up the numbers and start from the leftmost (highest-value) digit:

Compare 8,342 and 8,329:

• Thousands: $8 = 8$ (tie)
• Hundreds: $3 = 3$ (tie)
• Tens: $4 > 2$

$8{,}342 > 8{,}329$

Order smallest to largest: 1,204 | 986 | 12,480 | 1,200

Step 1: count digits — 986 has 3 digits (smallest); 12,480 has 5 digits (largest).

Ordered: 986 < 1,200 < 1,204 < 12,480

Rounding Whole Numbers

Rounding rules:

1. Find the place you are rounding to
2. Look at the digit immediately to the right
3. If that digit is 5 or greater: round up (increase the target digit by 1)