scientific notation

Scientific notation is a compact way to write very large or very small numbers as a coefficient times a power of ten: a × 10^n, where a is at least 1 and less than 10. Instead of writing 0.0000000004 you write 4 × 10^(−10), which is easier to read and compare.

The power of ten records the size, and the coefficient records the significant digits. A positive exponent shifts the decimal point to the right (a big number); a negative exponent shifts it to the left (a small number). For example 6.022 × 10^23 is the digits 6022 followed by enough places to land at 23 digits before the decimal point.

The rule that the coefficient stays between 1 and 10 keeps each number written in exactly one way. If a calculation gives something like 35 × 10^4, you normalize it to 3.5 × 10^5. Multiplying and dividing such numbers is easy because you handle the coefficients and the powers of ten separately, using the product and quotient rules of exponents.