Conversion Results
Scientific Notation
1.23457 × 10⁸
From 123,456,789
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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
| Prefix | Symbol | Power | Decimal |
|---|---|---|---|
| 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 |
| Base | - | 10⁰ | 1 |
| Milli | m | 10⁻³ | 0.001 |
| Micro | μ | 10⁻⁶ | 0.000001 |
| Nano | n | 10⁻⁹ | 0.000000001 |
| Pico | p | 10⁻¹² | 0.000000000001 |
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
What is scientific notation?
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.
How do I convert a number to scientific notation?
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.
What is engineering notation?
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.
How do I multiply numbers in scientific notation?
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.
How do I add/subtract numbers in scientific notation?
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: 2026-01-15
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How this works
Formulas follow standard definitions from the NIST Digital Library of Mathematical Functions and classical textbook derivations. Calculations run entirely in your browser. Where a closed-form solution exists, it is used; where an iterative or numerical method is required, the implementation is named on the page.
Sources
- [1]NIST Digital Library of Mathematical FunctionsAcademicdlmf.nist.govAccessed Apr 21, 2026
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