×10ⁿ

Math calculator

Scientific Notation Calculator

Rewrite a number as c × 10^e, expand scientific form, or add, subtract, multiply, and divide two scientific numbers.

Scientific notation4.5 × 10^3
Ordinary number4,500

Formulan = c × 10^e, with 1 ≤ |c| < 10 (or c = 0)
Calculation steps
  1. 4,500 = 4.5 × 10^3

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How it works

How to use this scientific notation calculator

  1. Choose To scientific, From scientific, or Operate.
  2. Enter an ordinary number, or a coefficient and integer exponent, or two scientific operands and an operation.
  3. Read the normalized c × 10^e form and the ordinary value.

Formula

The calculation formula

n = c × 10^e, with 1 ≤ |c| < 10 (or c = 0)
01

Find the exponent so the coefficient sits in [1, 10) or (−10, −1].

02

To expand, multiply the coefficient by 10 raised to the integer exponent.

03

To operate, convert both sides to ordinary numbers, compute, then normalize again.

Worked examples

Example calculations

To scientific notation

4500 = 4.5 × 10^3. Zero is written 0 × 10^0.

Multiply two scientific numbers

(2 × 10^3) × (3 × 10^2) = 6 × 10^5. The same identity holds after converting to 2000 × 300.

When to use it

Common use cases

  • Write 4500 as 4.5 × 10^3
  • Expand 4.5 × 10^3 back to 4500
  • Multiply 2 × 10^3 by 3 × 10^2 to get 6 × 10^5

Limits

Assumptions and limits

  • Normalized form uses 1 ≤ |c| < 10, except that 0 is 0 × 10^0.
  • Exponents must be integers. Coefficients may be any finite number; From mode also shows the normalized pair.
  • Arithmetic uses ordinary IEEE-754 numbers, then normalizes. Values outside the finite range are rejected.

Questions

Frequently asked questions

What counts as scientific notation here?

A coefficient times an integer power of 10, written c × 10^e. Engineering notation that forces multiples of three is not applied.

Why convert to ordinary numbers before operating?

Addition needs aligned exponents. Converting both sides, computing, and normalizing again matches the same result as aligning by hand, within floating-point limits.

Sources

Sources and review