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Scientific Notation Converter
Use this free scientific notation converter to turn any number into scientific notation, e-notation, or engineering notation — or to turn scientific notation back into a normal number. It handles very large and very small numbers, decimals, and negatives, and shows every form at once.
How it works
Scientific notation is a short way of writing very large or very small numbers. It writes a number as a coefficient multiplied by a power of ten: a × 10^b. The coefficient, a, is a number from 1 up to (but not including) 10, and the exponent, b, is a whole number that says how many places the decimal point moved. The number 123,456 becomes 1.23456 × 10^5, because moving the decimal point five places to the left gives 1.23456, and multiplying by 10^5 moves it five places back to the right.
The sign of the exponent tells you the size of the number at a glance. A positive exponent means a large number: 10^5 is 100,000, so 1.23456 × 10^5 is about a hundred thousand. A negative exponent means a small number: 10^-4 is 0.0001, so 4.5 × 10^-4 is 0.00045. An exponent of zero means the number is already between 1 and 10, so 7.3 × 10^0 is just 7.3. Scientists love this form because it makes the size of a number obvious — the exponent is the order of magnitude — and it makes multiplication and division easy, since you multiply the coefficients and add the exponents.
E-notation is the same idea written for keyboards and screens. Instead of the "× 10^" part, it uses the letter e: 1.23456 × 10^5 becomes 1.23456e5, and 4.5 × 10^-4 becomes 4.5e-4. Calculators, spreadsheets, and programming languages all use e-notation, because a superscript exponent cannot be typed on a normal keyboard. The value is identical — only the packaging changes — so this converter shows both forms for every number you enter.
Engineering notation is a close cousin with one extra rule: the exponent must be a multiple of 3. That means the coefficient can run from 1 to 999 instead of 1 to 10, and every step lines up with a metric prefix. An exponent of 3 is kilo, 6 is mega, 9 is giga, −3 is milli, and −6 is micro. So 123,456 in engineering notation is 123.456 × 10^3 — the same as 123.456 kilo — and 0.00045 is 450 × 10^-6, or 450 micro. Engineers prefer this form because it matches the units on real instruments and components: resistors in kilo-ohms, capacitors in microfarads, frequencies in megahertz.
Converting back is the reverse move. Take the coefficient and move its decimal point by the exponent: right for a positive exponent, left for a negative one. For 4.5 × 10^-4, move the point four places left — 0.45, 0.045, 0.0045, 0.00045 — and you are done. Pick the "scientific notation → number" direction in this converter, enter the coefficient and the exponent, and it expands the number out in full, with commas, so you can read it plainly.
Scientific notation shows up wherever numbers get extreme: astronomy (the distance to a star in kilometers), chemistry (the mass of a single atom in grams), electronics (a current of millionths of an amp), and finance (national budgets in the trillions). It is also the standard way to write very precise measurements, because the coefficient carries exactly the digits that were measured, and nothing else. When you see a number like 6.02 × 10^23 — Avogadro's number, the count of atoms in a mole — you are seeing scientific notation doing exactly the job it was built for.
Worked example
Convert 123,456 to scientific notation, and convert 0.00045 the same way.
Step 1: For 123,456, move the decimal point left until one digit remains before it — five places — giving a coefficient of 1.23456 and an exponent of 5.
Step 2: Write it as 1.23456 × 10^5. In e-notation that is 1.23456e5, and in engineering notation it is 123.456 × 10^3.
Step 3: For 0.00045, move the decimal point right until one digit remains before it — four places — giving a coefficient of 4.5 and an exponent of −4.
Step 4: Write it as 4.5 × 10^-4. In e-notation that is 4.5e-4, and in engineering notation it is 450 × 10^-6.
Check the first answer by moving the point back: 1.23456 with the point moved five places right is 123,456. Check the second the same way: 4.5 with the point moved four places left is 0.00045. Both answers are exact, and both are far shorter than writing out all the zeros.
FAQ
What is scientific notation?
Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of 10. For example, 123,456 becomes 1.23456 × 10^5, and 0.00045 becomes 4.5 × 10^-4. It keeps very large and very small numbers short and readable.
What is the difference between scientific notation and e-notation?
They are the same value written differently. Scientific notation uses a times-ten-to-the-power symbol, as in 1.23456 × 10^5, while e-notation replaces that with the letter e, as in 1.23456e5. Calculators and spreadsheets use e-notation because it fits on one line.
What is engineering notation?
Engineering notation is like scientific notation, except the exponent is always a multiple of 3, so the coefficient can run from 1 to 999. That lines up with metric prefixes: 10^3 is kilo, 10^6 is mega, 10^-3 is milli, and 10^-6 is micro. For example, 123,456 is 123.456 × 10^3 in engineering notation.
How do you convert scientific notation back to a normal number?
Move the decimal point in the coefficient by the exponent: a positive exponent moves it right, a negative exponent moves it left. For 4.5 × 10^-4, move the point four places left to get 0.00045. This converter does it for you — just pick the scientific-to-number direction.