Scientific Notation: How to Write, Read, and Convert It
Scientific notation writes a number as a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer. This guide shows how to convert large and small numbers, how to read them back, and how to handle the E-notation calculators use.
Scientific notation writes any number as
a × 10ⁿ, where the coefficientasits between one and ten and the exponentnis a whole number. A positive exponent marks a large number, a negative exponent marks a small one, and the exponent counts how far the decimal point moved.
The scientific notation calculator converts in either direction instantly. The rest of this page shows how it works.
What the form means
Every number in scientific notation has exactly two parts. The coefficient is a number with one nonzero digit before the decimal point, and the rule that keeps the notation standard is that its absolute value stays at or above one and below ten. The other part is a power of ten whose exponent tells you how far the decimal point moved.
That constraint is what separates correct scientific notation from a number that merely has a power of ten attached. Two writings can equal the same value while only one is proper, because the other has a coefficient that is not below ten.
Converting a large number
Place the decimal point so the coefficient lands between one and ten. There is one nonzero leading digit, so the point goes right after it. Then count how many places you slid the decimal to get there. The original point sits at the far right of a whole number, so you move it left, and a large number always gives a positive exponent.
A quick check confirms it: a positive exponent always means a value bigger than one.
Converting a small number
The goal is the same, a coefficient between one and ten. Find the first nonzero digit and place the decimal after it. This time you slide the point to the right, and moving right gives a negative exponent. The sign rule mirrors the large-number case, because a value smaller than one always carries a negative exponent.
The same procedure handles any magnitude. The table below pairs standard form with its scientific notation and the decimal moves between them.
Converting back to standard form
Reading scientific notation back into a plain number reverses the moves, and the exponent tells you both direction and distance. A positive exponent moves the decimal point right that many places, filling with zeros. A negative exponent moves it left, again filling with zeros.
6.022 × 10²³ → move 23 right → 602,200,000,000,000,000,000,000 1.6 × 10⁻⁹ → move 9 left → 0.0000000016
A useful sanity check is the zero exponent. Ten to the zero power is one, so anything times it is just the coefficient by itself.
E-notation on calculators
Calculators and programming languages rarely print superscripts, so they use E-notation instead. The letter E or e stands for "times ten to the power of," and the number after it is the exponent. It is the same notation, only typed on one line, so when a calculator answer shows an E, read it as a power of ten and convert it the same way.
Our scientific notation calculator accepts both the superscript form and E-notation as input.
Quick reference
A large number gives a positive exponent, counted by sliding the decimal left. A small number gives a negative exponent, counted by sliding it right. To convert back, a positive exponent moves the point right and a negative one moves it left. To combine numbers, multiply or divide the coefficients and add or subtract the exponents. For conversions in either direction without counting zeros by hand, use the scientific notation calculator.
form = a × 10ⁿ, with 1 ≤ |a| < 10 large → positive exponent, count moves left small → negative exponent, count moves right
Common questions
It keeps very large and very small numbers readable and avoids miscounting zeros. A short coefficient with an exponent is faster and less error-prone to write than a long string of digits, and the exponent makes the magnitude obvious at a glance.
A positive exponent marks a number greater than one, and a negative exponent marks a number between zero and one. The size of the exponent is how many places the decimal point moved from the coefficient.
Multiply the coefficients and add the exponents. If the new coefficient lands outside the standard range, renormalize so it sits between one and ten again. Dividing works the same way, except you subtract the exponents.
