Scientific Notation Calculator
Convert between standard and scientific notation
Scientific notation expresses very large or very small numbers in the form a × 10n, where a is a number between 1 and 10, and n is an integer exponent.
This calculator converts in both directions:
- Standard → Scientific: Enter any decimal number and get its scientific notation form
- Scientific → Standard: Enter a coefficient and exponent to get the full number
Scientific notation is essential in physics, chemistry, astronomy, and engineering — anywhere you deal with numbers that would be unwieldy to write out in full, like the distance to the Andromeda galaxy (2.537 × 1022 m) or the mass of a proton (1.673 × 10−27 kg).
Example
Convert 0.000045 to scientific notation:
Move decimal 5 places right → coefficient = 4.5, exponent = −5
Result: 4.5 × 10−5
Convert 3,200,000: move decimal 6 places left → 3.2 × 106
Frequently Asked Questions
What is scientific notation?
Scientific notation is a way of writing numbers as a product of a coefficient (between 1 and 10) and a power of 10. For example, 5,400,000 = 5.4 × 10⁶ and 0.00032 = 3.2 × 10⁻⁴. It makes very large or very small numbers easier to read and work with.
How do I convert a number to scientific notation?
Move the decimal point until you have a number between 1 and 10. Count how many places you moved it — that's the exponent. Moving left gives a positive exponent; moving right gives a negative one. Example: 0.0056 → move right 3 places → 5.6 × 10⁻³.
How do I convert scientific notation to a standard number?
Multiply the coefficient by 10 raised to the exponent. For 3.7 × 10⁴: multiply 3.7 by 10,000 = 37,000. For 2.1 × 10⁻³: multiply 2.1 by 0.001 = 0.0021. Alternatively, move the decimal point left (negative exponent) or right (positive exponent) by the number of places equal to the exponent.
What is E notation?
E notation is shorthand for scientific notation used in calculators and programming. '3.2E6' means 3.2 × 10⁶ and '4.5E-5' means 4.5 × 10⁻⁵. It's used in Python, JavaScript, and most programming languages. 'E' stands for 'exponent'.
How do you multiply numbers in scientific notation?
Multiply the coefficients and add the exponents. (3 × 10⁴) × (2 × 10³) = (3 × 2) × 10^(4+3) = 6 × 10⁷. If the resulting coefficient is ≥10 or <1, adjust: 15 × 10⁴ = 1.5 × 10⁵.
How do you divide numbers in scientific notation?
Divide the coefficients and subtract the exponents. (9 × 10⁶) ÷ (3 × 10²) = (9÷3) × 10^(6−2) = 3 × 10⁴.
What does a negative exponent mean?
A negative exponent means the number is smaller than 1. 10⁻³ = 1/10³ = 0.001. So 6.5 × 10⁻³ = 0.0065. Negative exponents are common in chemistry (atomic masses, concentrations) and physics (Planck's constant, electron charge).
Why is scientific notation useful?
It simplifies very large and very small numbers, making them easier to compare, multiply, and divide. It also makes precision explicit — 3.00 × 10⁸ shows three significant figures, whereas '300,000,000' doesn't indicate which digits are significant.
What are significant figures in scientific notation?
The number of digits in the coefficient represents significant figures. 4.50 × 10³ has 3 significant figures. 4.5 × 10³ has 2. Scientific notation makes it unambiguous — unlike 4500, which could have 2, 3, or 4 significant figures.
How is scientific notation used in everyday science?
Astronomy uses it for distances (Earth to Sun: 1.496 × 10¹¹ m). Chemistry uses it for Avogadro's number (6.022 × 10²³ mol⁻¹). Biology uses it for bacteria sizes (~1 × 10⁻⁶ m). Computer science uses it for storage sizes and processor speeds.