Place Value

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. Understanding place value is crucial for understanding how numbers are composed and how to perform operations with them.

Understanding Place Value

To understand place value, we need to look at the positions of the digits in a number. The positions are called ones, tens, hundreds, thousands, and so on, from right to left. For example, in the number 3,682:

The digit 2 is in the ones place
The digit 8 is in the tens place
The digit 6 is in the hundreds place
The digit 3 is in the thousands place

Place Value Chart

A place value chart is a helpful tool for visualizing the value of each digit in a number. It organizes the digits by their place value to help understand the magnitude of each digit in the number.

Thousands	Hundreds	Tens	Ones
3	6	8	2

Example Problems

Let's look at some example problems to apply our understanding of place value.

Problem 1:

What is the value of the digit 5 in the number 7,549?

Answer: The digit 5 is in the hundreds place, so its value is 500.

Problem 2:

Write the number 4,327 in expanded form.

Answer: 4,000 + 300 + 20 + 7

Place Value and Operations

Understanding place value is essential for performing addition, subtraction, multiplication, and division with larger numbers. It helps us to correctly align the digits and perform operations on numbers with multiple place values.

Practice Problems

Now that we've covered the basics of place value, it's time to practice with some problems. Here are a few to get started:

What is the value of the digit 9 in the number 9,876?
Write the number 6,205 in expanded form.
Add 3,421 and 2,367.

Remember to pay attention to the place value of each digit when solving these problems!

◂Math Worksheets and Study Guides Fifth Grade. Place Value

The resources above cover the following skills:

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 5 Focal Points (NCTM)

Number and Operations: Building on their work in grade 4, students extend their understanding of place value to numbers through millions and millionths in various contexts. They apply what they know about multiplication of whole numbers to larger numbers. Students also explore contexts that they can describe with negative numbers (e.g., situations of owing money or measuring elevations above and below sea level).

Place Value

Understanding Place Value

Place Value Chart

Example Problems

Problem 1:

Problem 2:

Place Value and Operations

Practice Problems

[Place Value] Related Worksheets and Study Guides:

◂Math Worksheets and Study Guides Fifth Grade. Place Value

The resources above cover the following skills: