Place Value Calculator

Break down any number into its place values and see the expanded form with step-by-step details.

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Expanded Form
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Step-by-Step Breakdown

Understanding Place Value

Place value is the value of each digit in a number based on its position. In our base-10 (decimal) number system, each position represents a power of 10. Moving left from the decimal point, each position is 10 times greater. Moving right, each position is 10 times smaller.

Place Value Chart

Ones (10^0)

The rightmost position before the decimal point. Value: 1.

Example: 5 in 345 = 5 x 1 = 5

Tens (10^1)

Second position from the right. Value: 10.

Example: 4 in 345 = 4 x 10 = 40

Hundreds (10^2)

Third position from the right. Value: 100.

Example: 3 in 345 = 3 x 100 = 300

Tenths (10^-1)

First position after the decimal point. Value: 0.1.

Example: 7 in 0.7 = 7 x 0.1 = 0.7

Hundredths (10^-2)

Second position after the decimal. Value: 0.01.

Example: 5 in 0.05 = 5 x 0.01 = 0.05

Thousandths (10^-3)

Third position after the decimal. Value: 0.001.

Example: 9 in 0.009 = 9 x 0.001

Expanded Form

Expanded form shows a number as the sum of its place values. For example, 3,456 in expanded form is 3,000 + 400 + 50 + 6. This representation helps students understand the contribution of each digit to the total value of the number.

Why Place Value Matters

  • Foundation for understanding addition, subtraction, multiplication, and division algorithms.
  • Essential for rounding numbers correctly.
  • Helps with comparing and ordering numbers.
  • Basis for understanding different number systems (binary, hexadecimal).
  • Critical for scientific notation and significant figures.