Place value is the value of a digit based on its position in a number. In our decimal number system, each digit's place value is ten times the place value of the digit to its right. The places in a number are ones, tens, hundreds, thousands, and so on, moving from right to left.

To understand place value, let's take the number 327 as an example. In this number, the digit 7 is in the ones place, the digit 2 is in the tens place, and the digit 3 is in the hundreds place. This means that the value of 7 is 7 ones, the value of 2 is 2 tens (or 20), and the value of 3 is 3 hundreds (or 300).

A place value chart is a helpful tool for understanding the value of digits in a number. It organizes the digits by their place value, making it easier to identify and calculate their values.

Thousands | Hundreds | Tens | Ones |
---|---|---|---|

3 | 2 | 7 |

Let's look at a few examples to further understand place value:

- The number 456 has a 4 in the hundreds place, a 5 in the tens place, and a 6 in the ones place. This means the value of 4 is 400, the value of 5 is 50, and the value of 6 is 6.
- In the number 8092, the 8 is in the thousands place, the 0 is in the hundreds place, the 9 is in the tens place, and the 2 is in the ones place. This means the value of 8 is 8000, the value of 0 is 0, the value of 9 is 90, and the value of 2 is 2.

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Study GuidePlace Value Worksheet/Answer key

Place Value Worksheet/Answer key

Place Value Worksheet/Answer key

Place Value Worksheet/Answer key

Place Value Worksheet/Answer key

Place Value Worksheet/Answer key

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Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Connections to the Grade 3 Focal Points (NCTM)

Number and Operations: Building on their work in grade 2, students extend their understanding of place value to numbers up to 10,000 in various contexts. Students also apply this understanding to the task of representing numbers in different equivalent forms (e.g., expanded notation). They develop their understanding of numbers by building their facility with mental computation (addition and subtraction in special cases, such as 2,500 + 6,000 and 9,000 - 5,000), by using computational estimation, and by performing paper-and-pencil computations.