Exponential Notation Calculator

Very large and very small numbers are easier to read in exponential notation: 0.000 000 47 becomes 4.7 × 10⁻⁷, or 470 nano-units in engineering form. This calculator converts any number between standard, scientific, E-notation and engineering notation at the significant figures you choose, and names the matching SI prefix — useful for science homework, electronics and spreadsheets.

Four ways to write the same number

SI prefixes

The SI system also includes larger and smaller prefixes, including ronna, quetta, ronto and quecto added in 2022. Note that k is lowercase for kilo and M uppercase for mega, while m is milli — case matters.

Significant figures in exponential form

Exponential notation makes significant figures unambiguous. Written as 4700, it’s unclear whether the zeros are significant; written as 4.7 × 10³ there are two significant figures, and 4.700 × 10³ shows four. When converting a measurement, keep the same number of significant figures as the original — the calculator uses the figures you type unless you choose a fixed number.

Worked example: capacitors and distances

A capacitor marked 470 nF is 470 × 10⁻⁹ F = 4.70 × 10⁻⁷ F = 0.000 000 470 F — the calculator shows all these forms from any one of them. At the other end of the scale, the average distance from Earth to the Sun, about 149,600,000 km, is 1.496 × 10⁸ km in scientific notation, 149.6 × 10⁶ km in engineering notation, and 1.496E+8 in a spreadsheet.

Exponent rules

Where you’ll see each form

• Scientific notation: science classes, textbooks and research papers.
• E-notation: calculator displays (4.7E-7), Excel and Google Sheets, CSV files and code.
• Engineering notation and SI prefixes: electronics (µF, kΩ, MHz), computing (GB, ns) and engineering drawings.
• Standard form: everyday numbers, finance and when readers aren’t used to exponents.

Converting by hand

1. Move the decimal point until one non-zero digit is in front of it.
2. Count the places moved: that is the exponent.
3. Moving left (for big numbers) makes the exponent positive; moving right (for small numbers) makes it negative.
4. Keep the significant figures from the original number.
5. For engineering notation, choose the nearest lower exponent that is a multiple of 3 and adjust the mantissa (it will be between 1 and 999).

Example: 0.000 470 → move the point four places right → 4.70 × 10⁻⁴. In engineering notation that is 470 × 10⁻⁶, or 470 µ.

Common mistakes

• Writing 47 × 10⁻⁸ as scientific notation — the coefficient must be between 1 and 10 (4.7 × 10⁻⁷).
• Confusing m (milli, 10⁻³) with M (mega, 10⁶).
• Typing 10E5 on a calculator when you mean 1 × 10⁵ (10E5 is 10 × 10⁵ = 10⁶).
• Dropping significant zeros: 4.70 and 4.7 are different measurements.
• Forgetting that a negative exponent means a small number, not a negative one.

Orders of magnitude in everyday science

Comparing exponents gives a quick sense of scale: a hair is roughly a hundred times wider than the wavelength of light and roughly a million times wider than an atom.

E-notation in spreadsheets and code

Spreadsheets switch long numbers to E-notation automatically — 123456789012 may display as 1.23457E+11. Widen the column or apply a number format to show all digits. Most programming languages read E-notation directly: 4.7e-7 in JavaScript, Python or C is the same value as 0.00000047. Large identifiers such as barcodes or account numbers should be stored as text so they are never converted.

The practice pack

The optional pack includes printable conversion worksheets with answer keys, an SI prefix chart with examples, an exponent rules card and an Excel converter sheet. The converter on this page is free.

AI-assisted content

This page was drafted with AI assistance and reviewed by Kedop.