MultiConvers

Scientific Notation Calculator

Write a large or tiny decimal as a × 10^n with one digit before the point, or turn a coefficient and exponent back into ordinary form.

How to use

  1. To encode: enter the full decimal (32000 or 0.005).
  2. Read a × 10^n with 1 ≤ |a| < 10.
  3. To decode: enter a coefficient and an integer exponent; the decimal comes back.
  4. If you type 32 × 10^3, the page normalizes to 3.2 × 10^4. Engineering steps of 3 are not used.

How it works

Normalized scientific notation is a × 10^n with one non-zero digit left of the point (except for zero). 32,000 moves the point four places left: 3.2 × 10^4. 0.005 moves three places right: 5 × 10^−3. 6.02 × 10^23 is already normalized.

Zero is 0 × 10^0. There is no unique coefficient for zero.

Engineering notation keeps exponents as multiples of 3 (12.5 × 10^3). This page will rewrite that as 1.25 × 10^4. Calculator “SCI” mode on a handheld is the same idea as here.

Overflow is rejected. This is a display conversion, not a log, and not the exponent calculator’s 2^8 = 256 (that is a power, not a × 10^n spelling).

E-notation 3.2e4 is the same number as 3.2 × 10^4. A leading plus on the exponent is optional. Negative coefficients stay negative: −3.2 × 10^4 is −32000, not a sign on the exponent. Rounding the coefficient is display only — 1.23456789 × 10^5 may show fewer digits than you typed.

Formula

x = a × 10^n,  with  1 ≤ |a| < 10  (or x = 0)
32000 = 3.2 × 10^4
0.005 = 5 × 10^−3

Worked examples

  • A large integer

    32000 → 3.2 × 10^4

  • A small decimal

    0.005 → 5 × 10^−3

Decimals written in normalized form

DecimalScientific notation
320003.2 × 10^4
0.0055 × 10^−3
0.000424.2 × 10^−4
6.02e236.02 × 10^23
00 × 10^0
12.5 × 10^31.25 × 10^4

Useful notes

  • Normalized form, not engineering notation.
  • Exponent must be an integer when converting from scientific notation.
  • Zero → 0 × 10^0.

FAQ

How do I convert a number to scientific notation?

Move the decimal point so one non-zero digit sits to the left of it. The number of places you moved is the exponent — positive if you moved left, negative if you moved right.

How do I convert scientific notation back to a decimal?

Move the decimal point by the exponent. 3.2 × 10^4 moves four places right → 32000. A negative exponent moves left.

What is the scientific notation for 0?

0 × 10^0. There is no unique normalized coefficient for zero, so the exponent is taken to be 0.

How is 0.00042 written?

4.2 × 10^−4.

Is 12.5 × 10^3 acceptable?

As an input it is rewritten to 1.25 × 10^4. Normalized form wants |a| < 10.

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