Scientific Notation Calculator

Convert numbers to and from scientific notation. Perform arithmetic operations with scientific notation and engineering notation.

Conversion Results

Scientific Notation

1.23457 × 10⁸

From 123,456,789

Coefficient1.23456789
Exponent8
Engineering123.457 × 10⁶

Decimal to Scientific Notation

Scientific Notation

1.23457 × 10⁸

Engineering Notation

123.457 × 10⁶

E-Notation

1.23456789E8

Scientific Notation Operations

First Number

6.5 × 10⁶ = 6.5000e+6

Scientific Notation Rules

Multiplication

(a × 10ᵐ) × (b × 10ⁿ) = (a × b) × 10ᵐ⁺ⁿ

Multiply coefficients, add exponents

Division

(a × 10ᵐ) ÷ (b × 10ⁿ) = (a ÷ b) × 10ᵐ⁻ⁿ

Divide coefficients, subtract exponents

Addition / Subtraction

Convert to same exponent first, then add/subtract coefficients

Standard Form

Coefficient must be ≥ 1 and < 10

Metric Prefixes

PrefixSymbolPowerDecimal
TeraT10¹²1,000,000,000,000
GigaG10⁹1,000,000,000
MegaM10⁶1,000,000
Kilok10³1,000
Base-10⁰1
Millim10⁻³0.001
Microμ10⁻⁶0.000001
Nanon10⁻⁹0.000000001
Picop10⁻¹²0.000000000001

Common Examples

Speed of Light

299,792,458 m/s

2.998 × 10⁸ m/s

Earth's Mass

5,972,000,000,000,000,000,000,000 kg

5.972 × 10²⁴ kg

Electron Mass

0.000000000000000000000000000000911 kg

9.11 × 10⁻³¹ kg

Avogadro's Number

602,214,076,000,000,000,000,000

6.022 × 10²³

?How Do You Convert to Scientific Notation?

Scientific notation expresses numbers as a x 10^n where 1 <= |a| < 10. Convert: move decimal until one digit before it, exponent = positions moved (right = negative, left = positive). Example: 4,500,000 = 4.5 x 10^6. For 0.00032 = 3.2 x 10^-4. Useful for very large or small numbers.

What is Scientific Notation?

Scientific notation is a way of expressing numbers as a product of a coefficient (between 1 and 10) and a power of 10. It provides a compact way to write very large or very small numbers and simplifies calculations with such numbers. Scientific notation is standard in science, engineering, and technical fields.

Key Facts About Scientific Notation

  • Format: a x 10^n where 1 <= |a| < 10
  • Positive exponent: large number (10^6 = 1,000,000)
  • Negative exponent: small number (10^-6 = 0.000001)
  • Multiply: multiply coefficients, add exponents
  • Divide: divide coefficients, subtract exponents
  • E notation: 4.5E6 means 4.5 x 10^6
  • Engineering notation uses exponents divisible by 3
  • Used in science for very large (distances) or small (atoms) values

Quick Answer

Scientific notation expresses numbers as a x 10^n where 1 <= |a| < 10. Convert: move decimal until one digit before it, exponent = positions moved (right = negative, left = positive). Example: 4,500,000 = 4.5 x 10^6. For 0.00032 = 3.2 x 10^-4. Useful for very large or small numbers.

Frequently Asked Questions

Scientific notation is a way of writing very large or very small numbers concisely. A number is expressed as a coefficient between 1 and 10 multiplied by a power of 10. For example, 6,500,000 becomes 6.5 × 10⁶ and 0.00032 becomes 3.2 × 10⁻⁴.
Move the decimal point until you have a number between 1 and 10. Count how many places you moved: right movement = negative exponent, left movement = positive exponent. Example: 0.00045 → move decimal 4 places right → 4.5 × 10⁻⁴.
Engineering notation is similar to scientific notation but uses exponents in multiples of 3 (... -6, -3, 0, 3, 6, 9 ...). This aligns with metric prefixes (kilo = 10³, mega = 10⁶, milli = 10⁻³, micro = 10⁻⁶) making it practical for engineering.
Multiply the coefficients and add the exponents. (a × 10ᵐ) × (b × 10ⁿ) = (a × b) × 10⁽ᵐ⁺ⁿ⁾. Then adjust if needed so coefficient is between 1 and 10. Example: (2 × 10³) × (3 × 10⁴) = 6 × 10⁷.
First convert both numbers to the same power of 10. Then add or subtract the coefficients. Keep the same exponent. Finally, adjust to proper scientific notation if needed. Example: 5×10³ + 3×10² = 5×10³ + 0.3×10³ = 5.3×10³.

Last updated: 2025-01-15