Scientific Notation Calculator
Convert to Scientific Notation
Easily convert any number to scientific notation, engineering notation, and E-notation formats.
Conversion Results
1.23 × 10⁶
Number Magnitude Visualization:
Scientific notation expresses numbers as a coefficient multiplied by a power of 10.
What is Scientific Notation?
Scientific Notation is a way to express very large or very small numbers in a compact, standardized format. It's written as a product of two numbers: a coefficient and a power of 10, where the coefficient is between 1 and 10.
Scientific Notation Formats
Scientific Notation
1 ≤ |a| < 10
Most common format
Engineering Notation
Exponent multiple of 3
Preferred in engineering
E-Notation
Computer-friendly format
Used in programming
Standard Form
Original format
With commas/decimals
Conversion Rules
1. Large Numbers (≥ 10)
Move decimal point left, positive exponent:
1,230,000 → 1.23 × 10⁶
2. Small Numbers (< 1)
Move decimal point right, negative exponent:
0.0000456 → 4.56 × 10⁻⁵
3. Numbers Between 1 and 10
No movement needed, exponent is 0:
7.89 → 7.89 × 10⁰
Real-World Applications
Astronomy & Space Science
- Distances between stars: Light-years in scientific notation
- Planetary masses: Handling extremely large numbers
- Cosmic measurements: Galaxy sizes and distances
- Space exploration: Rocket fuel calculations
Physics & Chemistry
- Atomic scales: Avogadro's number (6.022 × 10²³)
- Quantum mechanics: Planck's constant (6.626 × 10⁻³⁴)
- Chemical reactions: Mole calculations
- Electromagnetism: Coulomb's constant
Engineering & Technology
- Computer memory: Bytes, gigabytes, terabytes
- Electrical engineering: Resistance and capacitance values
- Nanotechnology: Molecular scale measurements
- Data storage: File sizes and capacities
Biology & Medicine
- Cell biology: Cell counts and microorganisms
- Genetics: DNA base pairs and genome sizes
- Microbiology: Virus particle counts
- Pharmacology: Drug dosage calculations
Common Scientific Notation Examples
| Standard Form | Scientific Notation | Engineering Notation | E-Notation |
|---|---|---|---|
| 1,230,000 | 1.23 × 10⁶ | 1.23 × 10⁶ | 1.23E+6 |
| 0.0000456 | 4.56 × 10⁻⁵ | 45.6 × 10⁻⁶ | 4.56E-5 |
| -7,890,000 | -7.89 × 10⁶ | -7.89 × 10⁶ | -7.89E+6 |
| 602,200,000,000,000,000,000 | 6.022 × 10²³ | 602.2 × 10²¹ | 6.022E+23 |
Step-by-Step Conversion Process
Example 1: Convert 123,000 to Scientific Notation
- Identify the number: 123,000
- Move decimal point: 123,000 → 1.23000
- Count decimal places moved: 5 places left
- Determine exponent: Positive 5 (moved left)
- Write result: 1.23 × 10⁵
Example 2: Convert 0.000456 to Scientific Notation
- Identify the number: 0.000456
- Move decimal point: 0.000456 → 4.56
- Count decimal places moved: 4 places right
- Determine exponent: Negative 4 (moved right)
- Write result: 4.56 × 10⁻⁴
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Frequently Asked Questions (FAQs)
Q: What's the difference between scientific and engineering notation?
A: Scientific notation uses exponents that can be any integer, while engineering notation uses exponents that are multiples of 3 (10³, 10⁶, 10⁹, etc.).
Q: Can scientific notation handle zero?
A: Yes, zero can be written as 0 × 10⁰, but typically we just write 0 since it doesn't need scientific notation.
Q: How do I convert scientific notation back to standard form?
A: Move the decimal point right for positive exponents, left for negative exponents, by the number of places equal to the absolute value of the exponent.
Q: What is the advantage of using scientific notation?
A: It makes very large and very small numbers easier to read, write, and compare. It also reduces errors in calculations with extreme values.
Master scientific notation with Toolivaa's free Scientific Notation Calculator, and explore more mathematical tools in our Math Calculators collection.