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Convert numbers between standard notation and scientific notation (coefficient x 10^exponent).
Scientific Notation:
Format: a x 10^n where 1 ≤ |a| < 10
Convert to scientific: find exponent = floor(log10(|x|)), then a = x / 10^n
Examples:
5,400,000 = 5.4 x 10^6
0.000045 = 4.5 x 10^(-5)
Scientific notation expresses numbers as a x 10^n where 1 ≤ |a| < 10. It is used to write very large or very small numbers compactly. For example, the speed of light is 3 x 10^8 m/s.
A positive exponent means move the decimal right (large number). A negative exponent means move decimal left (small number). For example, 2.5 x 10^3 = 2500, and 2.5 x 10^(-3) = 0.0025.
E notation is a compact form of scientific notation used in calculators and programming: 2.5E3 means 2.5 x 10^3 = 2500. The E stands for 'exponent'.
Scientific notation makes very large or small numbers easier to write and compare. For example, the mass of an electron (0.000000000000000000000000000000911 kg) is more clearly written as 9.11 x 10^(-31) kg.
Multiply the coefficients and add the exponents: (a x 10^m) x (b x 10^n) = (ab) x 10^(m+n). Then adjust if the new coefficient is not between 1 and 10.