Scientific Notation Calculator — Free Online Calculator & Guide

How Sci Notation Works

a × 10ⁿ where 1 ≤ |a| < 10

Scientific notation expresses numbers as a coefficient between 1 and 10 multiplied by a power of 10. It is used to represent very large or very small numbers compactly. The exponent tells you how many places the decimal point moves: positive exponents for large numbers, negative exponents for small numbers.

a

Coefficient — A number between 1 and 10 (or between -1 and -10 for negative numbers). Also called the significand or mantissa.

n

Exponent — The power of 10. Positive for large numbers (decimal moves left), negative for small numbers (decimal moves right).

× 10ⁿ

Power of 10 — Indicates the scale factor. Each increment of n multiplies the coefficient by 10.

How to Use

1. Choose your conversion direction: decimal to scientific or scientific to decimal.
2. For decimal to scientific: enter any number and view it in scientific notation, E notation, and with an animated decimal point movement.
3. For scientific to decimal: enter the coefficient and exponent separately and view the standard decimal form.
4. The "Decimal Moves" counter tells you exactly how many places the decimal point moved and in which direction.

Understanding the Result

Scientific notation is a compact way to write very large or very small numbers. Instead of writing 6,022,140,760,000,000,000,000,000 (Avogadro's number), you write 6.022 × 10²³. The decimal point "jumps" left for large numbers (positive exponent) and right for small numbers (negative exponent). The coefficient is always between 1 and 10 (exclusive of 10). For example, 4,500 becomes 4.5 × 10³ — the decimal moved 3 places left. And 0.0045 becomes 4.5 × 10⁻³ — the decimal moved 3 places right. Zero is a special case expressed as 0 × 10⁰. E notation is a computer-friendly variant: 4.5e3 means 4.5 × 10³. Scientific notation is essential in physics (speed of light = 3 × 10⁸ m/s), chemistry (Avogadro's number = 6.022 × 10²³), astronomy (distance to Andromeda = 2.5 × 10⁶ light-years), and computer science (data sizes in bytes).

Frequently Asked Questions

How do I convert a decimal to scientific notation?

Move the decimal point so there is exactly one non-zero digit to its left. Count how many places you moved it. If you moved left, the exponent is positive. If right, the exponent is negative. Example: 0.0045 → move decimal 3 places right → 4.5 × 10⁻³. The calculator shows this step with an animation.

How do I convert scientific notation to decimal?

A positive exponent means move the decimal point right (making a larger number). A negative exponent means move it left (making a smaller number). Example: 4.5 × 10⁻³ → move decimal 3 places left → 0.0045. The number of places matches the absolute value of the exponent.

What is the difference between scientific notation and E notation?

They are equivalent. E notation replaces "× 10ⁿ" with "e±n" for compact display, especially in calculators and programming. For example, 4.5 × 10⁻³ = 4.5e-3. Both mean 4.5 × 10⁻³ = 0.0045. The "e" stands for "exponent" and is not related to Euler's number.

Sources

• Wikipedia - Scientific Notation
• NIST - Metric (SI) Prefixes