# Scientific Notation & Significant Figures Calculator

> Convert any number to scientific, E and engineering notation, count its significant figures, and round to a chosen number of sig figs — with a magnitude number line.

- **Category:** Math
- **Interactive calculator:** https://youcalc.com/en/math/scientific-notation/
- **Price:** Free, no sign-up required

## Overview

This calculator converts any number to scientific, E and engineering notation, counts its significant figures, and rounds to a chosen number of sig figs. Use it to check your working in science or maths class, prepare values for lab reports, or simply understand the scale of very large or very small numbers.

## How to read your result

The headline result shows your number in standard scientific notation — mantissa × 10^exponent — with the same value also displayed in engineering notation (exponent a multiple of 3) and compact E-notation. The stats row beneath lists the number of significant figures the calculator detected and the value rounded to your chosen sig-fig count. The magnitude number line at the bottom marks where your number sits on a scale from 10^−15 to 10^15.

## Method

To convert to scientific notation the calculator finds the exponent as floor(log₁₀|x|) and divides x by 10^exponent to get the mantissa. Engineering notation uses the same approach but rounds the exponent down to the nearest multiple of 3. Significant-figure counting applies the standard rules: the algorithm strips the sign, identifies the first non-zero digit as the start of the significant range, and for bare integers without a decimal point drops trailing zeros before counting. Rounding to n sig figs is done by computing the scale factor 10^(n − ceil(log₁₀|x|)), multiplying, rounding to the nearest integer, and dividing back.

## Example

- **Setup:** Enter 12345 as the number and 3 as the significant-figures target.
- **Result:** The calculator returns scientific notation 1.2345 × 10^4, engineering notation 12.345 × 10^3, E-notation 1.2345e4, detects 5 significant figures in the input, and rounds to 3 sig figs giving 12300.

## Frequently asked questions

### What is scientific notation and why is it useful?

Scientific notation expresses a number as a mantissa between 1 and 10 multiplied by a power of ten (for example 6.02 × 10^23). It makes arithmetic on very large or very small numbers manageable, removes ambiguity about trailing zeros, and is the standard format in science, engineering and computing.

### What is the difference between scientific and engineering notation?

In scientific notation the exponent can be any integer and the mantissa is always between 1 and 10. In engineering notation the exponent is always a multiple of 3, so the mantissa ranges between 1 and 1000. Engineering notation aligns with SI prefixes such as kilo (10^3), mega (10^6) and micro (10^−6), making it easier to read units.

### How do I count significant figures correctly?

All non-zero digits are significant. Zeros between non-zero digits are always significant. Leading zeros (before the first non-zero digit) are never significant. Trailing zeros in a whole number without a decimal point are ambiguous and treated as non-significant; a trailing decimal point (writing "1500." instead of "1500") signals that those zeros are significant. In scientific notation every digit of the mantissa is significant.

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## Sources

- https://www.calculatorsoup.com/calculators/math/scientificnotation.php
- https://www.khanacademy.org/math/arithmetic-home/arith-review-decimals/arithmetic-significant-figures-tutorial/v/significant-figures

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Interactive version: https://youcalc.com/en/math/scientific-notation/ · From YouCalc — https://youcalc.com