Scientific Notation

Scientific notation is a method of writing numbers in which a number is divided into two parts: a mantissa (or coefficient) that typically falls between 1 and 10, and 10 raised to a power (exponent) that indicates how many times the number has been scaled up or down. For example, 4,300 can be written as 4.3 × 10³, while 0.00072 is written as 7.2 × 10⁻⁴.

This notation is used when working with very large or very small numbers, such as distances between stars or the size of an atom. It reduces errors that arise from writing out many digits and makes it easier to compare measurements.

General Form

The standard form is a × 10ⁿ, where n is a positive or negative integer and a is a number between 1 (inclusive) and 10 (exclusive). When these conditions on a are strictly met, the notation is called normalized scientific notation. If the exponent is positive, the number is greater than or equal to 10; if negative, the number is a fraction less than 1.

Calculation

When multiplying two numbers in scientific notation, the mantissas are multiplied and the exponents are added. When dividing, the mantissas are divided and the exponents are subtracted. When adding or subtracting, the exponents must first be made equal. The result is then adjusted so that the mantissa returns to the range 1–10.

Relationship to Significant Figures

Scientific notation shows how many significant figures a measurement contains. For example, 1.20 × 10³ indicates three significant figures, whereas 1.2 × 10³ indicates two. For this reason, scientists and engineers rely on it to communicate the precision of a measurement.

Related Forms

Engineering notation is a variant in which the exponent of 10 is restricted to multiples of 3 (10³, 10⁶, 10⁻³), aligning with SI prefixes such as kilo, mega, and milli. Calculators and computer programs often write the form using E, for example 4.3E3, which means 4.3 × 10³.