Scientific Notation Converter
Convert numbers between standard decimal form and scientific notation instantly. Essential for handling very large or very small values in science and engineering.
About this calculator
Scientific notation expresses any number as a × 10^b, where 1 ≤ |a| < 10 and b is an integer exponent. To convert a standard number to scientific notation, move the decimal point until only one non-zero digit sits to its left, and count the moves — each move to the left increases the exponent by 1, and each move to the right decreases it by 1. For example, 0.000047 = 4.7 × 10^(−5), and 3,200,000 = 3.2 × 10^6. Converting back to standard form means shifting the decimal in the direction indicated by the exponent. Scientific notation prevents errors when writing many zeros and makes multiplication and division of extreme values much simpler by allowing you to handle the coefficients and exponents separately.
How to use
Example 1 — Large number: The distance from Earth to the Sun is about 149,600,000 km. Enter 149600000. The converter identifies 8 digits before the decimal and returns 1.496 × 10^8. Example 2 — Small number: A red blood cell is about 0.000008 meters wide. Enter 0.000008. The converter shifts the decimal 6 places right and returns 8 × 10^(−6). Example 3 — Entering scientific notation: Type 6.022e23 (Avogadro's number) and the tool returns 602,200,000,000,000,000,000,000.
Frequently asked questions
How do I convert a very small decimal number to scientific notation?
Count how many places you must move the decimal point to the right to get a number between 1 and 10 — that count becomes the negative exponent. For example, with 0.00000392, move the decimal 6 places right to get 3.92, so the result is 3.92 × 10^(−6). A useful memory trick: if the original number is less than 1, the exponent is negative; if it's greater than or equal to 10, the exponent is positive. Double-check by expanding back: 3.92 × 10^(−6) = 0.00000392.
Why is scientific notation used in science and engineering?
Extreme values — like the mass of an electron (0.00000000000000000000000000000091 kg) or the number of atoms in a mole (602,200,000,000,000,000,000,000) — are impractical to write or read in standard form. Scientific notation compresses these into compact, readable expressions (9.1 × 10^(−31) kg and 6.022 × 10^23) that are easy to compare, multiply, and divide. It also makes the order of magnitude immediately visible, which is critical when estimating or checking the reasonableness of a result. Most scientific calculators and programming languages use this format for very large or very small outputs.
How do you multiply or divide numbers in scientific notation?
To multiply, multiply the coefficients and add the exponents: (a × 10^m) × (b × 10^n) = (a × b) × 10^(m+n). For example, (3 × 10^4) × (2 × 10^3) = 6 × 10^7. To divide, divide the coefficients and subtract the exponents: (a × 10^m) / (b × 10^n) = (a/b) × 10^(m−n). If the resulting coefficient falls outside the range [1, 10), adjust it and correct the exponent accordingly — for instance, 15 × 10^3 becomes 1.5 × 10^4. This makes arithmetic with astronomical or atomic-scale numbers far more manageable than working in standard form.