Scientific Notation Calculator

Turn a decimal into scientific notation, or expand it back. The steps are shown.

Smart Tips

• Normalized form uses a coefficient from 1 up to, but not including, 10. Zero is 0 × 10⁰.

• Moving the decimal left makes the exponent positive. Moving it right makes the exponent negative.

• An unnormalized coefficient such as 45.6 × 10² is expanded, then reported in normalized form.

• The exponent must stay inside ±1,000, and the number can have at most 100 digits.

The Formula

number = a × 10ⁿ with 1 ≤ |a| < 10

a Coefficient
One nonzero digit before the decimal point

n Exponent
Places the decimal point moved

left Positive exponent
The original number was at least 10

right Negative exponent
The original number was smaller than 1

The coefficient is written in the shortest form. Trailing zeros that would matter for significant figures belong on the significant-figures page.

Key Insights

Both directions

A decimal becomes a × 10ⁿ. A coefficient and an exponent expand back to standard form, with the normalized notation beside it.

Zero is special

Zero is written 0 × 10⁰. There is no nonzero digit to put in front of the decimal point.

Steps stay visible

Each conversion lists where the decimal point moved and which way.

Not significant figures

This page drops trailing zeros in the coefficient. Counting those zeros is a different tool.

Frequently Asked Questions

A number written a × 10ⁿ where a is at least 1 and less than 10, or −1 down to but not including −10. Zero is 0 × 10⁰.

If you move it left, the exponent is positive. If you move it right, the exponent is negative. The steps on the result card say how many places and which direction.

The page still expands the coefficient you typed by the exponent you typed. It then reports the normalized coefficient and the adjusted exponent. 45.6 × 10² is 4560, which normalizes to 4.56 × 10³.

No. The coefficient is the shortest decimal that matches the value. Zeros that are significant in a lab measurement are handled on the significant-figures calculator.

The exponent, including one already written in the decimal, must be from −1,000 through 1,000. The number can have at most 100 digits.

The form a × 10ⁿ, with one nonzero digit before the decimal point, follows OpenStax College Algebra 2e, section 1.2, Exponents and Scientific Notation.

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Result

Enter values to calculate

Coefficient

Exponent

Note:The coefficient is normalized so one nonzero digit sits before the decimal point, or the value is 0 × 10⁰. Trailing zeros are not treated as significant figures. The exponent is limited to ±1,000.