Scientific Notation Converter (Free, Both Ways)

Use this free scientific notation converter to switch between standard form and scientific notation in both directions. Enter a number to write it as a × 10ⁿ, or enter a coefficient and exponent to expand it back to standard form.

How to use the converter

1. Pick a direction: Standard → Scientific or Scientific → Standard.
2. Enter your value(s).
3. Read the converted result and the step-by-step explanation of how the decimal point moved.

What is scientific notation?

Scientific notation writes a number as a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer. It makes very large and very small numbers easy to read and compare.

Frequently asked questions

How do you write a number in scientific notation?

Move the decimal point so one nonzero digit is in front of it; the number of places you moved becomes the exponent (positive for large numbers, negative for small ones).

What does a negative exponent mean?

In normalized scientific notation, a negative exponent means the number’s absolute value is between 0 and 1. For example, 4.2 × 10⁻⁴ = 0.00042 and −4.2 × 10⁻⁴ = −0.00042. The minus sign on a coefficient describes the number’s sign; the exponent describes its scale.

Does it convert both directions?

Yes, standard to scientific and scientific back to standard, each with the steps shown.

Read the full lesson: learn the method step by step.

Worked conversions in both directions

For 53,000, move the decimal point four places left to get 5.3. Compensate with 10⁴: 53,000 = 5.3 × 10⁴. For 0.00042, move it four places right to get 4.2, so 0.00042 = 4.2 × 10⁻⁴.

To expand 6.7 × 10³, move the decimal three places right: 6,700. To expand 6.7 × 10⁻³, move it three places left: 0.0067. Keep a negative coefficient negative throughout the conversion.

Check the coefficient and exponent

For every nonzero number, the coefficient’s absolute value must be at least 1 and less than 10. Although 53 × 10³ equals 53,000, its normalized form is 5.3 × 10⁴. Numbers from 1 up to, but not including, 10 use exponent 0 because 10⁰ = 1.

Zero is a special case: it cannot have a coefficient satisfying 1 ≤ |a| < 10. Do not force zero into that normalization rule. Keep any measurement units beside the result, and round only when your assignment specifies the required precision.