Place Value: Ones, Tens, Hundreds, ...
Each digit has a place value: ones (10โฐ), tens (10ยน), hundreds (10ยฒ), thousands (10ยณ). Expanded form: 345 = 3ร100 + 4ร10 + 5ร1. Decimals: tenths (10โปยน), hundredths (10โปยฒ).
Did our AI summary help? Let us know.
345 = 3ร100 + 4ร10 + 5ร1. Expanded form. 0.25 = 2ร0.1 + 5ร0.01. Decimal places. Place value chart: align digits by place.
Ready to run the numbers?
Why: Place value is the foundation of our number system. Understanding it enables regrouping, rounding, and operations. Expanded form shows the structure.
How: Write the number. Each digit: value = digit ร 10^place. Integer places: ones, tens, hundreds, ... Decimal places: tenths, hundredths, thousandths, ...
Run the calculator when you are ready.
Enter Number
Place Value Chart
Place Value Contributions
Value Proportions
๐ Step-by-Step Breakdown
For educational and informational purposes only. Verify with a qualified professional.
๐งฎ Fascinating Math Facts
Expanded form: digit ร 10^place
โ Place value
Ones=10โฐ, tens=10ยน, hundreds=10ยฒ
โ Powers of 10
๐ Key Takeaways
- โข Our number system is base-10 (decimal) and positional
- โข Each digit's value = digit ร 10^place (ones, tens, hundreds, thousands...)
- โข Expanded form writes the number as a sum of place values (e.g., 345 = 300 + 40 + 5)
- โข Word form spells the number in words (e.g., three hundred forty-five)
๐ก Did You Know?
๐ How Place Value Works
In 345, the 3 is in the hundreds place (3ร100=300), the 4 is in the tens place (4ร10=40), and the 5 is in the ones place (5ร1=5). So 345 = 300 + 40 + 5.
For decimals, 0.456 has 4 tenths (0.4), 5 hundredths (0.05), and 6 thousandths (0.006). So 0.456 = 4/10 + 5/100 + 6/1000.
๐ Worked Example: 1,234
Standard: 1,234
Expanded: 1000 + 200 + 30 + 4
Word: one thousand two hundred thirty-four
๐ Real-World Applications
๐ฐ Finance
Reading large numbers, currency, budgets.
๐ Measurement
Understanding decimal precision (mm, cm, m).
๐ข Education
Foundation for arithmetic and algebra.
โ ๏ธ Common Mistakes to Avoid
- Confusing place and value: In 345, the 3 is in the hundreds place; its value is 300.
- Forgetting zero placeholders: In 205, the 0 holds the tens place.
- Decimal alignment: 0.5 is 5 tenths, not 5 hundredths.
โ FAQ
What is place value?
The value of a digit based on its position. In 345, the 3 has value 300, the 4 has value 40, the 5 has value 5.
What is expanded form?
A number written as the sum of its place values. 1,234 = 1000 + 200 + 30 + 4.
What is word form?
The number spelled in words. 1,234 = one thousand two hundred thirty-four.
๐ Summary
Place value is the foundation of our number system. Understanding expanded and word form builds number sense for all future math.
โ ๏ธ Disclaimer: Word form follows American English. Very large numbers may be truncated.
Related Calculators
Long Addition Calculator
Free long addition calculator with step-by-step carrying and regrouping. Add up to 10 numbers in column format. Supports decimal addition in advanced mode....
MathematicsAbsolute Change Calculator
Calculate absolute and relative change between two values. Get direction (increase/decrease), percentage impact, and step-by-step solutions. Simple mode for...
MathematicsAbsolute Value Calculator
Calculate the absolute value |x| of any number. Simple mode for basic |x|; advanced mode for |ax+b| expressions. Get distance from zero, step-by-step...
MathematicsAdding & Subtracting Fractions Calculator
Add and subtract fractions with least common denominator (LCD). Simple mode for two fractions; advanced mode for mixed numbers and 3+ fractions. Step-by-step...
MathematicsAddition Calculator
Add two or more numbers with this free addition calculator. Get the sum, carry detection for column addition, and step-by-step solutions. Simple mode for two...
MathematicsArithmetic Mean Calculator
Calculate the arithmetic mean (average) of a set of numbers. Simple mode for basic mean; advanced mode adds weighted mean and trimmed mean. Step-by-step...
Mathematics