Express very large or small numbers in scientific notation, or convert scientific notation to standard form. Useful in science, engineering, and mathematics.
Scientific notation is a method of expressing very large or small numbers concisely. It is written in the form a × 10ⁿ, where a is a number between 1 and 10, and n is an integer. For example, 300,000,000 is expressed as 3.0 × 10⁸. It is widely used in scientific fields such as physics, chemistry, and astronomy.
To convert a standard number to scientific notation, move the decimal point after the first non-zero digit. Use a negative exponent for rightward moves and positive for leftward moves. Examples: 0.00045 = 4.5 × 10⁻⁴, 56000 = 5.6 × 10⁴
To convert scientific notation to standard form, move the decimal point by the number indicated by the exponent. Positive exponents move right, negative move left. 3.2 × 10⁵ = 320000, 7.1 × 10⁻³ = 0.0071
Engineering notation is a variation where exponents are always multiples of 3. This aligns with SI unit prefixes like kilo (10³), mega (10⁶), giga (10⁹), making it preferred in engineering. Example: 47000 = 47 × 10³ (engineering) vs 4.7 × 10⁴ (scientific)
To multiply numbers in scientific notation, multiply the mantissas and add exponents: (2 × 10³) × (3 × 10⁴) = 6 × 10⁷. For division, divide mantissas and subtract exponents: (8 × 10⁶) ÷ (2 × 10²) = 4 × 10⁴. Addition and subtraction require matching exponents first.
Essential for handling extreme values: Earth-Sun distance in astronomy (1.496 × 10⁸ km), Avogadro's number in chemistry (6.022 × 10²³), electron mass in physics (9.109 × 10⁻³¹ kg). Also used in computer science for floating-point representation.