Scientific Notation Calculator

Convert a decimal into normalized scientific notation, or start from a coefficient and an integer exponent to get the decimal back.

How it works

Normalized scientific notation writes a non-zero number as a × 10^n where 1 ≤ |a| < 10 and n is an integer. 32,000 is 3.2 × 10^4 because the point moved four places. 0.005 is 5 × 10^−3. Zero is written 0 × 10^0.

If you enter a coefficient outside 1…10, such as 32 × 10^3, the result is normalized to 3.2 × 10^4. Overflow is rejected instead of showing Infinity.

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

Useful notes

Engineering notation (exponents in steps of 3) is not used here.
The exponent must be a whole number when you convert from scientific notation.

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.

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