Understanding Place Value up to Ten Thousands

In math, every digit in a number has a specific value based on its position. This is called place value. As numbers get larger, we add new places to the left. For four-digit and five-digit numbers, we use the thousands and ten-thousands places.

The Place Value Chart

Let's look at the number $13{,}456$. We can break it down into its different place values from right to left:

• 6 is in the ones place (Value: $6$)
• 5 is in the tens place (Value: $50$)
• 4 is in the hundreds place (Value: $400$)
• 3 is in the thousands place (Value: $3{,}000$)
• 1 is in the ten-thousands place (Value: $10{,}000$)

Standard Form and Expanded Form

There are two common ways to write numbers:

Standard Form: This is the normal way we write numbers using just digits. Example: $3{,}625$

Expanded Form: This is writing a number as an addition problem to show the value of each digit. Example: $3{,}625 = 3{,}000 + 600 + 20 + 5$

If a number has a zero in one of its places, you simply skip that place in expanded form. For example, in the number $7{,}403$, there are $0$ tens:

• Standard Form: $7{,}403$
• Expanded Form: $7{,}000 + 400 + 3$

Practice Examples

Question: What is the value of the digit $3$ in $13{,}456$? Answer: The $3$ is in the thousands place, so its value is $3{,}000$.

Question: Write $5{,}000 + 200 + 60 + 1$ in standard form. Answer: Combine the values to make the number $5{,}261$.