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How It Works
- 1.calculators.scientific-notation.moveDecimalPoint
- 2.Count places moved = exponent (left = positive)
- 3.Result: 2.998 × 10^8
Powers of 10 Reference
Operation Rules
स्रोत और कार्यप्रणाली
a × 10ⁿ where 1 ≤ |a| < 10Scientific notation conversion
How to Use the Scientific Notation Calculator
The scientific notation calculator converts numbers to and from scientific notation, performs arithmetic with numbers in scientific notation, and displays results in multiple formats including E-notation and engineering notation.
What is Scientific Notation?
Scientific notation expresses numbers as a coefficient between 1 and 10 multiplied by a power of 10. It makes very large or very small numbers easier to work with. For example, the speed of light (299,792,458 m/s) becomes 2.998 × 10⁸ m/s.
Converting to Scientific Notation
- Move the decimal point until you have a number between 1 and 10
- Count how many places you moved the decimal
- If you moved left, the exponent is positive; if right, it's negative
Example: 0.00045 → Move decimal 4 places right → 4.5 × 10⁻⁴
E-Notation
E-notation is a computer-friendly way to write scientific notation. The "E" represents "× 10^". For example:
- 3.5 × 10⁸ = 3.5E8
- 2.1 × 10⁻⁵ = 2.1E-5
Engineering Notation
Engineering notation is similar to scientific notation but uses exponents that are multiples of 3, corresponding to metric prefixes (kilo, mega, giga, milli, micro, nano). For example: 45,000 = 45 × 10³ (not 4.5 × 10⁴).
Operations in Scientific Notation
- Multiplication: Multiply coefficients, add exponents. (2 × 10³) × (3 × 10⁴) = 6 × 10⁷
- Division: Divide coefficients, subtract exponents. (6 × 10⁸) ÷ (2 × 10³) = 3 × 10⁵
- Addition/Subtraction: Convert to same exponent, then add/subtract coefficients.
Related Calculators
For tracking precision in calculations, use our sig fig calculator. For exponent calculations, try our exponent calculator.
अक्सर पूछे जाने वाले प्रश्न
Move the decimal point until you have one non-zero digit to its left. Count how many places you moved. If you moved left, the exponent is positive; if right, negative. Example: 45000 becomes 4.5 × 10⁴ (moved 4 places left). 0.0023 becomes 2.3 × 10⁻³ (moved 3 places right).
Scientific notation uses exponents from -∞ to ∞ with one digit before the decimal. Engineering notation restricts exponents to multiples of 3 (matching SI prefixes like kilo, mega, milli). Example: 45,000 is 4.5 × 10⁴ in scientific notation but 45 × 10³ in engineering notation.
Multiply the coefficients and add the exponents. For (3 × 10⁴) × (2 × 10⁵): multiply 3 × 2 = 6, add exponents 4 + 5 = 9, result is 6 × 10⁹. If the coefficient exceeds 10, adjust: 15 × 10⁴ becomes 1.5 × 10⁵.
First convert both numbers to the same exponent, then add the coefficients. For (3 × 10⁴) + (5 × 10³): convert to (3 × 10⁴) + (0.5 × 10⁴) = 3.5 × 10⁴. Choose the larger exponent to minimize coefficient adjustments.
E notation is a computer-friendly way to write scientific notation. The E means "times 10 to the power of." For example, 3.5E8 means 3.5 × 10⁸ = 350,000,000. This format is used in calculators, programming languages, and spreadsheets.
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