🔢 Place value understanding by grade 2 predicts math achievement through grade 8 — it's the foundation everything else builds on. Students who can fluently decompose 3,456 into 3 thousands + 4 hundreds + 5 tens + 6 ones master multiplication 2× faster. Explore, quiz, and compare numbers interactively. Why foundational skills compound →
Place Value Chart
Interactive number explorer, quiz, and comparison tool for mastering place values
Interactive Place Value Chart
Hover over any column to highlight it. Each column shows the place name, power of 10, and an example value.
Number Explorer
Enter any number to see its place value breakdown, written form, expanded form, and more.
Place Value Quiz
Test your place value knowledge with 10 random questions!
Decimal Place Values
Place values extend to the right of the decimal point. Each position is 1/10 of the one before it.
Examples
0.5
5 tenths — like cutting a pizza into 10 slices and taking 5
0.25
2 tenths + 5 hundredths — a quarter of a dollar
3.14
3 ones + 1 tenth + 4 hundredths — approximately pi
Enter two numbers to align their place values side by side and see which is greater.
Frequently Asked Questions
What is place value in math?
Place value is the value of each digit in a number based on its position. For example, in the number 5,432, the digit 5 is in the thousands place, so its value is 5,000. The digit 4 is in the hundreds place (value 400), 3 is in the tens place (value 30), and 2 is in the ones place (value 2).
How do you read a place value chart?
Read a place value chart from left to right, starting with the largest place. Each column represents a power of 10. The digit in each column tells you how many of that place value the number contains. For example, if 7 is in the hundreds column, the number has 7 hundreds, or 700.
What is expanded form of a number?
Expanded form breaks a number into the sum of each digit multiplied by its place value. For example, 3,456 in expanded form is 3,000 + 400 + 50 + 6. This helps students understand that each digit contributes a different amount based on its position.
How do decimal place values work?
Decimal place values extend the place value system to the right of the decimal point. The first place after the decimal is tenths (1/10), then hundredths (1/100), then thousandths (1/1000). For example, in 3.456, the 4 is in the tenths place (0.4), 5 is in the hundredths place (0.05), and 6 is in the thousandths place (0.006).
Why is place value important?
Place value is the foundation of our number system. Understanding place value is essential for addition, subtraction, multiplication, division, rounding, comparing numbers, and working with decimals and large numbers. Without place value understanding, students cannot perform multi-digit arithmetic correctly.
Understanding Place Value: A Complete Guide
Place value is one of the most fundamental concepts in mathematics. Our number system is a base-10 (decimal) system, meaning each position in a number is worth 10 times the position to its right. This simple rule creates the entire structure for how we read, write, and work with numbers.
How the Place Value System Works
Every digit in a number has two properties: its face value (the digit itself, 0–9) and its place value (determined by its position). For the number 7,345:
7 is in the thousands place → value is 7,000
3 is in the hundreds place → value is 300
4 is in the tens place → value is 40
5 is in the ones place → value is 5
Whole Number Places
From right to left, whole number place values increase by a factor of 10: ones (10⁰), tens (10¹), hundreds (10²), thousands (10³), ten thousands (10⁴), hundred thousands (10⁵), millions (10⁶), ten millions (10⁷), hundred millions (10⁸), and billions (10⁹). Each group of three digits forms a period (ones, thousands, millions, billions).
Decimal Place Values
To the right of the decimal point, each position is worth 1/10 of the previous one: tenths (10⁻¹), hundredths (10⁻²), and thousandths (10⁻³). Understanding decimals is critical for working with money, measurements, and scientific data.
Tips for Teaching Place Value
Use physical manipulatives like base-10 blocks
Practice writing numbers in expanded form regularly
Play games that involve building numbers from digit cards
Use a place value chart as a visual reference during lessons
Connect place value to real-world contexts like money and measurement