Place Value Through Millions

Place value tells us the value of a digit based on its position in a number. As numbers get larger, we group them into "periods" separated by commas: the ones period, the thousands period, and the millions period.

The most important rule of place value is the base-ten rule: each place is exactly $10$ times the value of the place to its right.

The Place Value Chart

Let's look at the number $4{,}703{,}218$ on a place value chart:

• Millions: $4$ (Value: $4{,}000{,}000$)
• Hundred Thousands: $7$ (Value: $700{,}000$)
• Ten Thousands: $0$ (Value: $0$)
• Thousands: $3$ (Value: $3{,}000$)
• Hundreds: $2$ (Value: $200$)
• Tens: $1$ (Value: $10$)
• Ones: $8$ (Value: $8$)

In this number, the digit $7$ is in the hundred thousands place, so its value is $700{,}000$.

Three Ways to Write Numbers

You can represent large numbers in three different ways:

1. Standard Form: Writing the number using only digits and commas.
   • Example: $4{,}703{,}218$
2. Word Form: Writing the number out in words exactly as you would say it out loud.
   • Example: Four million, seven hundred three thousand, two hundred eighteen.
3. Expanded Form: Writing the number as an addition sentence that shows the value of each digit.
   • Example: $4{,}000{,}000 + 700{,}000 + 3{,}000 + 200 + 10 + 8$ (Note: We skip the ten thousands place because the digit is $0$.)

Example Problems

Example 1: What is the value of the digit 7 in $4{,}703{,}218$?

• Look at the position of the $7$. It is six spaces from the right, which is the hundred thousands place.
• Answer: The value is $700{,}000$.

Example 2: Write $2{,}045{,}300$ in expanded form.

• Break down the value of each non-zero digit:
  • $2$ is in the millions place: $2{,}000{,}000$
  • $4$ is in the ten thousands place: $40{,}000$
  • $5$ is in the thousands place: $5{,}000$
  • $3$ is in the hundreds place: $300$
• Answer: $2{,}000{,}000 + 40{,}000 + 5{,}000 + 300$

Example 3: Write "six hundred twelve thousand, four hundred nine" in standard form.

• First, write the thousands period: $612$
• Then, write the ones period: $409$
• Combine them with a comma.
• Answer: $612{,}409$