Scientific Notation Calculator

Scientific notation makes it easy to work with very large or very small numbers. This calculator converts between standard and scientific notation and performs arithmetic (add, subtract, multiply, divide) in scientific notation.

How to Use This Calculator

1. Convert to scientific notation: Enter any number → get it in a × 10ⁿ form.
2. Convert from scientific notation: Enter a and n → get the standard decimal number.
3. Arithmetic: Enter two numbers in scientific notation, select operation → get result in scientific notation.

Scientific Notation Format

a × 10ⁿ where 1 ≤ |a| < 10 and n is an integer.

• 93,000,000 = 9.3 × 10⁷
• 0.000045 = 4.5 × 10⁻⁵
• 1 = 1 × 10⁰

Conversion Method

Move the decimal until one non-zero digit is to the left. Count moves = exponent (positive for right → decimal moved left, negative for left → decimal moved right).

384,400 (distance to Moon in km): move decimal 5 places left → 3.844 × 10⁵

Arithmetic in Scientific Notation

Multiply: Multiply coefficients, add exponents.
(3 × 10⁴) × (2 × 10³) = 6 × 10⁷

Divide: Divide coefficients, subtract exponents.
(6 × 10⁸) ÷ (2 × 10³) = 3 × 10⁵

Add/Subtract: First make exponents equal, then add/subtract coefficients.

Common Mistakes to Avoid

• Not ensuring the coefficient is between 1 and 10 — 42 × 10³ is not proper scientific notation. It must be 4.2 × 10⁴.
• Adding exponents when adding numbers — Only multiply/divide operations combine exponents. Addition requires matching exponents first.
• Forgetting negative exponents mean small numbers — 10⁻⁶ = 0.000001, not a negative number.

Frequently Asked Questions

Why use scientific notation?

Numbers like the mass of an electron (0.000000000000000000000000000000911 kg = 9.11 × 10⁻³¹ kg) or the distance to Alpha Centauri (41,300,000,000,000,000 m = 4.13 × 10¹⁶ m) become unmanageable without it.

What is engineering notation?

Like scientific notation, but restricts exponents to multiples of 3 (corresponding to kilo, mega, giga, milli, micro, nano prefixes). 45,000 = 45 × 10³ = 45 kilo in engineering notation.

How does a calculator display scientific notation?

On most calculators, 6.02 × 10²³ displays as 6.02E23. The E means "× 10 to the power of."

Conclusion

Scientific notation is indispensable in physics, chemistry, astronomy, and engineering. Use this calculator to convert any number to standard form and perform arithmetic without worrying about zeros.

Related: Exponent Calculator | Big Number Calculator | Log Calculator