Place Value Calculator
Enter any whole number or decimal and this calculator shows the place value of every digit in the number. You get a position-by-position table (ones, tens, hundreds, thousands, and beyond), the expanded form, the word form, and a worked step panel. The result updates as you type.
What is place value?
Place value is the value a digit has because of its position in a number. In the decimal (base-10) system, every position is worth ten times the position immediately to its right. The digit 5 means five if it sits in the ones place, fifty in the tens place, five hundred in the hundreds place, and so on. Two numbers can share the same digits but have entirely different values if those digits are in different positions: 312 and 231 use the same three digits but stand for different amounts. Understanding place value is the foundation of arithmetic, because every operation from addition to long division works by manipulating digits position by position.
How to find the place value of any digit
Start at the decimal point, or at the right edge of a whole number if there is no decimal point. The rightmost whole-number digit is always in the ones place (10 to the power of zero, which equals 1). Moving one position to the left multiplies the place value by 10: tens, hundreds, thousands, and so on. Moving one position to the right of the decimal point divides by 10: tenths, hundredths, thousandths. To find the value of a specific digit, multiply that digit by the value of its position. For example, in 4,728 the digit 7 sits in the hundreds place, so its value is 7 x 100 = 700.
Expanded form and word form
Expanded form rewrites a number as the sum of each digit multiplied by its place value. For 4,728 the expanded form is 4,000 + 700 + 20 + 8. This makes the contribution of each digit explicit and is a key step in understanding column addition and subtraction. Word form is the same number written out as English words: four thousand, seven hundred twenty-eight. Knowing how to convert between standard, expanded, and word form is tested from elementary school through standardized exams, and it helps build intuition for estimation and rounding.
Decimal place values
The place value system extends seamlessly past the decimal point. The first digit to the right of the decimal point is the tenths position (worth 1/10), the second is hundredths (1/100), the third thousandths (1/1,000), and so on. A number like 3.145 expands to 3 + 1/10 + 4/100 + 5/1,000. Understanding decimal places is essential for money (cents are hundredths of a dollar), measurement (millimetres are thousandths of a metre), and scientific notation. When comparing or adding decimals, aligning numbers by their decimal point ensures matching place values line up correctly.
Place value positions and their powers of ten
| Position Name | Power of 10 | Numeric Value |
|---|---|---|
| Billions | 10⁹ | 1,000,000,000 |
| Hundred-Millions | 10⁸ | 100,000,000 |
| Ten-Millions | 10⁷ | 10,000,000 |
| Millions | 10⁶ | 1,000,000 |
| Hundred-Thousands | 10⁵ | 100,000 |
| Ten-Thousands | 10⁴ | 10,000 |
| Thousands | 10³ | 1,000 |
| Hundreds | 10² | 100 |
| Tens | 10¹ | 10 |
| Ones | 10⁰ | 1 |
| Tenths | 10⁻¹ | 0.1 |
| Hundredths | 10⁻² | 0.01 |
| Thousandths | 10⁻³ | 0.001 |
| Ten-Thousandths | 10⁻⁴ | 0.0001 |
Standard decimal (base-10) place value system. Each position is 10 times larger than the one to its right.
Frequently asked questions
What is the difference between place value and face value?
The face value of a digit is simply the digit itself, regardless of where it sits in a number. The place value is the digit multiplied by the value of its position. In the number 5,832, the digit 8 has a face value of 8 and a place value of 800 because it is in the hundreds position.
How do you find the place value of a digit in a decimal number?
Identify the position of the digit relative to the decimal point. The first position to the right of the decimal point is the tenths place (value 1/10), the second is hundredths (1/100), and so on. Multiply the digit by its positional value. For example, in 0.347 the digit 4 is in the hundredths place, so its place value is 4 x 1/100 = 0.04.
What comes after billions in the place value system?
After billions come ten-billions, hundred-billions, then trillions (10¹²). Beyond trillions are quadrillions (10¹⁵) and quintillions (10¹⁸). This calculator handles whole-number parts up to the quintillions place and decimal parts down to the ten-billionths place.
Why do zeros matter in place value?
Zeros act as placeholders. In the number 305, the zero holds the tens position open, making the 3 sit in the hundreds place and the 5 in the ones place. Without the placeholder zero, 305 would collapse to 35, an entirely different number. Similarly, 3.05 and 3.5 are different because the zero holds the tenths place in the first number.
What is expanded form and how does it relate to place value?
Expanded form is a way of writing a number as the sum of each digit multiplied by its place value. For example, 2,406 in expanded form is 2,000 + 400 + 0 + 6. It makes the role of each digit explicit and is especially useful for teaching column addition, subtraction with borrowing, and long multiplication, all of which operate one place at a time.
How does multiplying or dividing by 10 shift place values?
Multiplying a number by 10 shifts every digit one position to the left: the ones become tens, the tens become hundreds, and a new zero appears in the ones place. Dividing by 10 shifts every digit one position to the right: the ones become tenths and the tens become ones. This is why the base-10 system is so practical for mental arithmetic and estimation.