🔬 Scientific Notation

Convert numbers and perform arithmetic in scientific notation.

Enter any number (decimal, scientific, or E notation)

Conversions

How to Use This Calculator

This calculator converts numbers to and from scientific notation and handles arithmetic in scientific notation. You can type a regular number and get the scientific notation form, or enter a coefficient and exponent to see the standard decimal. For arithmetic, pick an operation and enter two values in whichever format you have.

To convert a number, type it in the conversion tab. The calculator shows both the scientific notation form and the E notation form (used in calculators and code).

For arithmetic, select the operation (multiply, divide, add, subtract) and enter each number. You can mix formats freely.

Read the coefficient and exponent in the result. Click Copy to grab the formatted output for use in reports or assignments.

If you get a result like 13.5 x 10^4, the calculator automatically normalises it to 1.35 x 10^5 for you.

The Rules of Scientific Notation

Standard form: a x 10^n (where 1 is less than or equal to |a| which is less than 10) Multiply: (a x 10^m)(b x 10^n) = (a x b) x 10^(m+n) Divide: (a x 10^m) / (b x 10^n) = (a/b) x 10^(m-n) Add/Sub: convert to same exponent first, then add or subtract coefficients Power: (a x 10^m)^p = a^p x 10^(m x p)

The coefficient must always sit between 1 and 10 (including 1 but excluding 10). The exponent tells you how far the decimal point has moved. A positive exponent means a large number; a negative exponent means a small fraction. After any calculation, check that your coefficient is still in the valid range and adjust the exponent if needed.

Worked Examples

0.0000456 to scientific notation4.56 x 10^-5

93,000,000 (Earth-Sun distance, miles)9.3 x 10^7

(3.2 x 10^4) x (2.5 x 10^3)8.0 x 10^7

(6.0 x 10^8) / (4.0 x 10^3)1.5 x 10^5

Where Scientific Notation Comes Up

In chemistry, you work with Avogadro's number (6.022 x 10^23) when counting particles and with concentrations as small as 10^-9 M in trace analysis. In physics, the charge of an electron is 1.6 x 10^-19 coulombs, and the speed of light is 3.0 x 10^8 m/s. Writing these out in full decimal form would be error-prone and hard to read, which is why every science and engineering textbook uses scientific notation.

In programming and data work, you will see E notation constantly. A value like 1.5E-4 in a spreadsheet or Python output is the same as 1.5 x 10^-4. Knowing how to read and convert between formats saves confusion when checking results from a simulation or a sensor reading that outputs very small voltages or very large byte counts.

Frequently Asked Questions

What is scientific notation?

Scientific notation expresses a number as a × 10^n where 1 ≤ |a| < 10. Example: 4,200,000 = 4.2 × 10⁶. It's used for very large or very small numbers.

How do I convert a decimal to scientific notation?

Move the decimal point until you have a number between 1 and 10. Count the moves: right = negative exponent, left = positive. 0.00045 → 4.5 × 10^-4.

How do I multiply numbers in scientific notation?

Multiply the coefficients and add the exponents: (a × 10^m) × (b × 10^n) = (a×b) × 10^(m+n). Then normalize so the coefficient is between 1 and 10.

How do I add numbers in scientific notation?

Convert both numbers to the same exponent, then add coefficients: 4.2×10³ + 3.0×10² = 4.2×10³ + 0.3×10³ = 4.5×10³.

What is E notation?

E notation is a computer-friendly shorthand for scientific notation: 4.2E6 means 4.2 × 10⁶. Used in calculators, spreadsheets, and programming languages.