Power of 10 Calculator

Calculate 10n for any exponent, view scientific notation equivalents, and explore common powers of 10.

Enter Exponent

Common Powers of 10

n10^nName

Result

10n
1,000,000
1 x 10^6
Exponent 6
Decimal Value 1,000,000
Scientific Notation 1 x 10^6
Number of Digits 7
Name Million
SI Prefix Mega (M)

Step-by-Step Solution

10^6 = 1,000,000

Understanding Powers of 10

Powers of 10 are the foundation of our decimal number system. Each power of 10 represents a position in a number: ones (100), tens (101), hundreds (102), and so on. Understanding powers of 10 is essential for scientific notation, metric conversions, and order-of-magnitude reasoning.

Key Concepts

Positive Exponents

10^n means 1 followed by n zeros. Each increase by 1 multiplies by 10.

10^3 = 1,000 (thousand)

Negative Exponents

10^(-n) = 1/10^n. Moves the decimal point n places left.

10^(-3) = 0.001 (thousandth)

Zero Exponent

Any non-zero number raised to the power 0 equals 1.

10^0 = 1

Scientific Notation

Scientific notation expresses numbers as a product of a coefficient (between 1 and 10) and a power of 10. For example, 6,500,000 = 6.5 x 106. This notation makes it easy to work with very large or very small numbers in science, engineering, and everyday calculations.

Metric (SI) Prefixes

The metric system uses powers of 10 to define prefixes for units of measurement:

  • Tera (T): 1012 = 1,000,000,000,000
  • Giga (G): 109 = 1,000,000,000
  • Mega (M): 106 = 1,000,000
  • Kilo (k): 103 = 1,000
  • Milli (m): 10-3 = 0.001
  • Micro (u): 10-6 = 0.000001
  • Nano (n): 10-9 = 0.000000001
  • Pico (p): 10-12 = 0.000000000001

Real-World Scale

  • 10-15 meters: Size of a proton (femtometer)
  • 10-9 meters: Size of a molecule (nanometer)
  • 100 meters: Human height
  • 107 meters: Diameter of Earth
  • 1011 meters: Distance from Earth to Sun
  • 1026 meters: Observable universe diameter

Properties of Powers of 10

  • 10^a x 10^b = 10^(a+b)
  • 10^a / 10^b = 10^(a-b)
  • (10^a)^b = 10^(a x b)
  • log10(10^n) = n