CalcRover

Scientific Notation Calculator

Convert both directions: any number into scientific notation (with the decimal-point moves counted out), and mantissa × 10^exponent back into a plain number. E-notation (4.2e-4) is shown for calculators and spreadsheets.

Number → scientific notation

Scientific notation → number

× 10^=

How scientific notation works

Scientific notation writes every number as m × 10^e with one non-zero digit before the point (1 ≤ |m| < 10). Count how many places the decimal point moves to get there: left moves make a positive exponent (big numbers), right moves negative (small ones).

It exists to keep extreme numbers readable and arithmetic manageable: multiplying means multiplying mantissas and ADDING exponents. Spreadsheets and calculators display the same thing as E-notation — 4.2E-4 is 4.2 × 10⁻⁴.

299,792,458 = 2.9979 × 10⁸ (point moved 8 left)
0.00042 = 4.2 × 10⁻⁴ (point moved 4 right)

Worked examples

Example 1: the speed of light

Write 299,792,458 m/s in scientific notation.

  1. Move the point left until one digit remains in front: 8 moves.
    2.99792458
  2. Left moves → positive exponent.
    2.9979 × 10⁸

≈ 3.0 × 10⁸ m/s — the physics-class constant.

Example 2: a small concentration

Write 0.00042 in scientific notation.

  1. Move the point right 4 places.
    4.2
  2. Right moves → negative exponent.
    4.2 × 10⁻⁴

4.2 × 10⁻⁴ (E-notation: 4.2e-4).

Example 3: multiplying in scientific notation

(3 × 10⁵) × (2 × 10⁻²) = ?

  1. Multiply mantissas, add exponents.
    3 × 2 = 6; 5 + (−2) = 3
  2. Combine.
    6 × 10³ = 6,000

6 × 10³ — no long multiplication needed.

FAQ

What's the difference between scientific and engineering notation?+

Engineering notation restricts the exponent to multiples of 3 so it lines up with unit prefixes: 47 × 10³ (47 k) instead of 4.7 × 10⁴. Same idea, different convention.

What does 4.2E-4 on my calculator mean?+

Exactly 4.2 × 10⁻⁴ = 0.00042. The E is just display shorthand for "times ten to the" — it has nothing to do with Euler's e.

Why must the mantissa be between 1 and 10?+

Convention for uniqueness — every number gets exactly one representation, so comparisons are instant: exponents first, mantissas second. 42 × 10³ is the same value but not normalized form.

How does scientific notation relate to significant figures?+

It makes them unambiguous: 3.00 × 10⁵ clearly has three significant figures, whereas 300,000 might have one or six. That's why labs report in scientific notation.

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