Logarithm Calculator
Calculate logarithms of any base. Compute log_b(x) = ln(x)/ln(b) for common, natural, and custom base logarithms.
Scientific Notation Converter
Convert numbers to and from scientific notation. Transform large or small numbers into a × 10^n format.
Any number, including e-notation (e.g. 6.02e23)
Enter a second number to compare magnitudes
Scientific Notation⧉
2.99792 × 10^8
Coefficient between 1 and 10, exponent = 8
E-Notation⧉
2.99792e8
Computer-friendly format
Engineering Notation⧉
299.792 × 10^6
Exponent is a multiple of 3
Coefficient⧉
2.99792
The mantissa of the number
Exponent (Power of 10)⧉
8
Order of magnitude
Decimal Form⧉
299,792,000
Standard decimal representation
Detected Sig Figs⧉
9
Significant figures in your input
Nearest SI Prefix⧉
giga (G, 10^9)
Closest metric prefix
Order of Magnitude Scale
Observable Universe10^26 m
Galaxy diameter10^21 m
Light-year10^16 m
Earth-Sun distance10^11 m
Earth radius10^7 m
Human height10^0 m
Ant length10^-3 m
Bacteria10^-6 m
Atom diameter10^-10 m
Proton radius10^-15 m
Planck length10^-35 m
Planning notes, formulas, and examples
About the Scientific Notation Converter
The Scientific Notation Converter transforms numbers between standard decimal form and scientific notation (a × 10^n). Scientific notation expresses any number as a coefficient between 1 and 10 multiplied by a power of ten.
This format is indispensable when working with extremely large numbers (speed of light: 3 × 10⁸ m/s) or extremely small numbers (electron mass: 9.109 × 10⁻³¹ kg). It keeps calculations manageable and highlights significant digits.
Our converter handles both directions: enter a decimal number to get scientific notation, or enter a coefficient and exponent to get the full decimal expansion. It also shows engineering notation (exponent is a multiple of 3) for practical use.
When This Page Helps
Manually converting large or tiny numbers is tedious and error-prone. This converter produces the correct coefficient, exponent, and full decimal expansion in both directions.
How to Use the Inputs
- Enter any number in standard decimal form.
- View the scientific notation (a × 10^n) result.
- See engineering notation and E-notation simultaneously.
- Or enter a coefficient and exponent to convert back to decimal.
- Use the converter to verify homework or data entry.
Formula used
a × 10^n
Where:
- a = coefficient (1 ≤ |a| < 10)
- n = integer exponent
- The number = a × 10^nExample Calculation
Result: 2.99792458 × 10⁸
The speed of light (299,792,458 m/s) moves the decimal 8 places left, giving coefficient 2.99792458 and exponent 8.
Tips & Best Practices
- A positive exponent means a large number (decimal moves right).
- A negative exponent means a small number (decimal moves left).
- Engineering notation uses exponents divisible by 3 (kilo, mega, giga).
- E-notation (2.998e8) is the computer-friendly form.
- The coefficient must be ≥ 1 and < 10 in proper scientific notation.
- Count the decimal shifts to find the exponent quickly.
Scientific Notation in Science
Physics, chemistry, and astronomy routinely use numbers spanning 60+ orders of magnitude, from the Planck length (1.6 × 10⁻³⁵ m) to the observable universe (8.8 × 10²⁶ m). Scientific notation makes these numbers comparable.
Significant Figures
Scientific notation naturally conveys precision. Writing 5.00 × 10³ indicates three significant figures, while 5 × 10³ indicates just one.
Computer Representation
Floating-point numbers in computers use a similar concept: a mantissa and exponent stored in binary, following the IEEE 754 standard.
Professionals in data science, engineering, and finance apply these calculations daily to model complex systems and test analytical hypotheses.
Sources & Methodology
Last updated:
Frequently Asked Questions
Scientific notation writes a number as a × 10^n where 1 ≤ |a| < 10 and n is an integer. It simplifies working with very large or very small numbers.
E-notation is the computer-friendly version: 2.998e8 means 2.998 × 10⁸. Programming languages and calculators commonly use this format.
Engineering notation restricts the exponent to multiples of 3, aligning with metric prefixes like kilo (10³), mega (10⁶), and giga (10⁹).
Move the decimal right until you have a number between 1 and 10: 4.2. You moved 4 places, so the exponent is −4. Result: 4.2 × 10⁻⁴.
Multiply the coefficients and add the exponents. (2 × 10³)(3 × 10⁴) = 6 × 10⁷. Adjust the coefficient if needed.
It prevents errors with zeros in large and small numbers, clarifies significant figures, and simplifies multiplication and division by using exponent arithmetic.
More in this topic
Significant Figures Calculator
Count significant figures and round numbers to a specified number of sig figs. Review how precision rules apply to each digit.