Definition
Scientific notation
Scientific notation writes a nonzero number as a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer.
What it means
Put exactly one nonzero digit before the decimal point. Then count how many places the decimal point moved: left gives a positive exponent for a large number; right gives a negative exponent for a small number. The new expression must equal the original number.
Remember it
One nonzero digit leads; the exponent counts the decimal-point jumps.
Example
Write 0.000482 in scientific notation. Move the decimal 4 places right to make 4.82, so use 10⁻⁴ to move it back: 0.000482 = 4.82 × 10⁻⁴.
Watch for
42 × 10³ equals 42,000, but it is not in scientific notation because 42 is not between 1 and 10 in size; write 4.2 × 10⁴.
Common mix-up
The exponent does not count the digits in the number; it counts place-value moves from the coefficient to the original number.
Exact meaning
For a nonzero real number, scientific notation is an equivalent expression a × 10ⁿ with integer n and 1 ≤ |a| < 10. The coefficient a carries the significant digits, and the power of ten fixes their place value.