Place Value Calculator

Identify place values of all digits in integers, whole numbers, or decimals using positional notation.

Identify place value of every digit in integers or decimals. See expanded form, word form, and visual chart.

?
Max 20 characters
Try:
help_outlineHow to Useexpand_more

Understanding Place Value

This calculator identifies the place value of every digit in your number using positional notation. Enter integers, whole numbers, or decimals to see each digit's position and value, plus get the number expressed in word form.

Integer Place Values (left of decimal):

Reading from right to left, each position is worth 10 times more:

  • Ones (1), Tens (10), Hundreds (100)
  • Thousands (1,000), Ten Thousands (10,000), Hundred Thousands (100,000)
  • Millions (1,000,000), Ten Millions, Hundred Millions
  • Billions (1,000,000,000) and beyond

Decimal Place Values (right of decimal):

Reading from left to right after the decimal point:

  • Tenths (0.1), Hundredths (0.01), Thousandths (0.001)
  • Ten Thousandths (0.0001), Hundred Thousandths (0.00001)
  • Millionths (0.000001) and smaller
infoWhat is Place Value Calculator?expand_more

Place value is the numerical value that a digit has based on its position in a number. Our decimal number system (base-10) uses positional notation where each place is worth 10 times the place to its right. This system allows us to represent any number using just ten digits (0-9).

For example, in the number 1,987,654,321, the leftmost 1 is in the billions place (worth 1,000,000,000), while the rightmost 1 is in the ones place (worth just 1). Understanding place value is essential for arithmetic operations, number comparison, and working with decimals.

Expanded form shows a number as the sum of each digit multiplied by its place value. For instance, 352 = 300 + 50 + 2, or more precisely: (3 × 100) + (5 × 10) + (2 × 1).

functionsFormulaexpand_more

Integer Place Values:

Ones = 10⁰ = 1

Tens = 10¹ = 10

Hundreds = 10² = 100

Thousands = 10³ = 1,000

... and so on (each ×10)

Decimal Place Values:

Tenths = 10⁻¹ = 0.1

Hundredths = 10⁻² = 0.01

Thousandths = 10⁻³ = 0.001

Ten Thousandths = 10⁻⁴ = 0.0001

... and so on (each ÷10)

Digit Value Formula:

Value = Digit × Place Value

Example: 7 in hundreds place = 7 × 100 = 700

lightbulbExamplesexpand_more

Example 1: 1,987,654,321

1 = Billions (1,000,000,000)

9 = Hundred Millions, 8 = Ten Millions, 7 = Millions

6 = Hundred Thousands, 5 = Ten Thousands, 4 = Thousands

3 = Hundreds, 2 = Tens, 1 = Ones

Word form: one billion nine hundred eighty-seven million...

Example 2: 0.123456789

1 = Tenths (0.1)

2 = Hundredths (0.02), 3 = Thousandths (0.003)

4 = Ten Thousandths, 5 = Hundred Thousandths

6 = Millionths, 7 = Ten Millionths, 8 = Hundred Millionths

9 = Billionths (0.000000009)

Example 3: 958.275

9 = Hundreds (900)

5 = Tens (50), 8 = Ones (8)

2 = Tenths (0.2), 7 = Hundredths (0.07), 5 = Thousandths (0.005)

Expanded: 900 + 50 + 8 + 0.2 + 0.07 + 0.005

Example 4: 100.001

1 = Hundreds (100)

0 = Tens (0), 0 = Ones (0)

0 = Tenths (0), 0 = Hundredths (0), 1 = Thousandths (0.001)

Expanded: 100 + 0.001 = 100.001

quizFAQexpand_more
Why is place value important?expand_more
Place value is fundamental to understanding our number system. It's essential for performing arithmetic operations (carrying in addition, borrowing in subtraction), comparing numbers, rounding, and working with decimals. Without understanding place value, operations like 23 + 45 would be confusing.
What is the difference between place and place value?expand_more
The 'place' refers to the position name (tens, hundreds, thousandths), while 'place value' is the actual numerical value of that position. For example, in 452, the digit 5 is in the tens place, and its place value is 50 (5 × 10).
How do decimal place values relate to fractions?expand_more
Decimal places represent fractions with denominators that are powers of 10. Tenths = 1/10, hundredths = 1/100, thousandths = 1/1000. So 0.25 is the same as 25/100 or 2/10 + 5/100.
What is expanded form?expand_more
Expanded form shows a number as the sum of each digit times its place value. For 3,527: expanded form is 3,000 + 500 + 20 + 7, or more explicitly (3 × 1,000) + (5 × 100) + (2 × 10) + (7 × 1).
Why do we use base-10 (decimal) system?expand_more
The base-10 system likely developed because humans have 10 fingers, making it natural for counting. In base-10, we use digits 0-9 and each place is worth 10 times the previous place. Other bases exist (binary uses base-2, hexadecimal uses base-16).