Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is written as a × 10ⁿ, where a (the coefficient or mantissa) is a number whose absolute value is at least 1 and less than 10, and n (the exponent) is an integer. For example, the speed of light (299,792,458 m/s) can be written as 2.99792458 × 10⁸.

E-notation is a compact way to represent scientific notation in computing and programming. Instead of writing "× 10ⁿ", the letter E (or e) is used. For example, 1.23e5 means 1.23 × 10⁵ = 123,000, and 4.56E-3 means 4.56 × 10^-3 = 0.00456. This format is widely used in programming languages like Python, JavaScript, C++, and in spreadsheet software like Excel.

To convert scientific notation to decimal, multiply the coefficient by 10 raised to the power of the exponent. If the exponent is positive, move the decimal point to the right by that many places (adding zeros if needed). If the exponent is negative, move the decimal point to the left. For example: 3.5 × 10⁴ → move decimal 4 places right → 35,000. 7.2 × 10^-3 → move decimal 3 places left → 0.0072.

To convert a decimal to scientific notation: (1) Move the decimal point so that exactly one non-zero digit appears before the decimal point. (2) Count how many places you moved the decimal — this becomes the exponent. (3) If you moved the decimal left, the exponent is positive; if you moved it right, the exponent is negative. Example: 45,600 → move decimal 4 places left → 4.56 × 10⁴. 0.00089 → move decimal 4 places right → 8.9 × 10^-4.

Significant figures (or significant digits) indicate the precision of a measurement. In scientific notation, all digits in the coefficient are considered significant. For example, 5.20 × 10³ has 3 significant figures (5, 2, and 0), while 5.2 × 10³ has only 2. The trailing zero in the first case indicates higher measurement precision. Scientific notation is excellent for clearly communicating significant figures without ambiguity.

Scientific notation is widely used in science and engineering to express extremely large or small values. Common applications include: Astronomy (distance to stars: 4.24 × 10¹⁶ m to Proxima Centauri), Physics (Planck constant: 6.626 × 10^-34 J·s), Chemistry (Avogadro's number: 6.022 × 10²³ mol^-1), Biology (cell sizes in micrometers), and Computer science (data storage capacities like 1 × 10¹² bytes for a terabyte).

Yes! The coefficient can be negative to represent negative numbers. For example, -3.2 × 10⁶ = -3,200,000. The rule for the absolute value still applies: the absolute value of the coefficient must be at least 1 and less than 10 (i.e., 1 ≤ |a| < 10). So you can have coefficients like -1.5, -9.99, -4.0, etc. The sign simply carries through to the final decimal value.

When the exponent is zero (n = 0), the scientific notation simplifies to just the coefficient itself, because 10⁰ = 1. For example, 5.67 × 10⁰ = 5.67 × 1 = 5.67. This is valid scientific notation and is sometimes used when a number's magnitude is close to 1, or to maintain consistent formatting in a dataset where other numbers require scientific notation.