Convert any decimal number to scientific notation, or convert a coefficient and exponent back into a standard decimal number.
This tool converts numbers between standard (decimal) form and scientific notation, and can perform arithmetic operations on numbers expressed in scientific notation. Scientific notation is used to conveniently express very large or very small numbers, common in physics, chemistry, engineering, and astronomy.
A number in scientific notation is written as a ร 10โฟ, where a is a number between 1 and 10 (the coefficient) and n is an integer (the exponent). To convert a standard number, count how many places the decimal point moves to get a single non-zero digit before the decimal.
Enter a standard number to convert it to scientific notation, or enter a number already in scientific notation to convert it back to standard form.
Example 1: 5,000,000 in scientific notation is 5 ร 10โถ.
Example 2: 0.00042 in scientific notation is 4.2 ร 10โปโด.
Why use scientific notation instead of writing out the full number? It makes extremely large or small numbers, like the distance to a star or the size of an atom, much easier to read, write, and compare without counting long strings of zeros.
What does a negative exponent mean? A negative exponent indicates the original number is smaller than 1 (a decimal), with the exponent showing how many places the decimal point moves to the left.
How do you multiply numbers in scientific notation? Multiply the coefficients together and add the exponents: (a ร 10แต) ร (b ร 10โฟ) = (a ร b) ร 10^(m+n).
How do you add numbers in scientific notation? First convert both numbers to the same exponent (power of 10), then add the coefficients directly while keeping the shared exponent.
Is scientific notation the same as engineering notation? They're similar but not identical โ engineering notation restricts exponents to multiples of 3 (matching metric prefixes like kilo, mega, milli), while scientific notation has no such restriction.