Place Value
Understanding the value of digits based on their position in a number
lessons (4)
Introduction to Place Value
Learn what place value means and how each digit in a number has a specific value based on its position.
Ones, Tens, and Hundreds
Learn how digits in different positions represent different values in our number system.
Expanded Form
Learn how to write numbers in expanded form by breaking them down into place values.
Comparing Whole Numbers
Learn how to compare whole numbers using place value and symbols like greater than, less than, and equal to.
Place value is the foundation of our number system, determining the value of each digit based on its position. In the number 5,432, the 5 represents 5,000 because it sits in the thousands place, while the 2 represents just 2 in the ones place. This positional system, using base 10, allows us to represent infinitely large numbers using only ten digits.
Understanding place value is essential for all arithmetic operations. When you add or subtract, you align numbers by place value. When you multiply by 10, you shift digits one place to the left. This concept extends to decimals, where positions to the right of the decimal point represent tenths, hundredths, and smaller fractions.
What Students Will Learn
- Identify the place value of any digit in whole numbers and decimals
- Read and write numbers in standard, expanded, and word form
- Compare and order numbers using place value understanding
- Round numbers to any given place value
- Apply place value concepts when adding, subtracting, and multiplying
Frequently Asked Questions
Why do we use a base-10 number system?
Humans likely developed base-10 because we have 10 fingers. Other bases exist: computers use base-2 (binary), and time uses base-60 for minutes and seconds.
What is the difference between a digit and a number?
A digit is a single symbol (0-9), while a number is made up of one or more digits. In 234, there are three digits forming one number.
How does place value work with decimals?
Places to the right of the decimal point represent fractions: tenths (0.1), hundredths (0.01), thousandths (0.001), and so on, each ten times smaller than the previous.