Scientific Notation Calculator

What is scientific notation?

Scientific notation writes any number as a × 10^n, where a is a coefficient with 1 ≤ |a| < 10 and n is an integer exponent. It is designed to compactly represent very large numbers (like the speed of light: 3.0 × 10^8 m/s) or very small numbers (like the charge on an electron: 1.6 × 10^−19 C).

How do you multiply numbers in scientific notation?

Multiply the coefficients and add the exponents: (a × 10^m) × (b × 10^n) = (a×b) × 10^(m+n). Then normalize the coefficient back into [1, 10) by adjusting the exponent. For example: (3 × 10^4) × (2 × 10^3) = 6 × 10^7.

How do you add or subtract in scientific notation?

First convert both numbers to the same exponent, then add the coefficients. For (3.2 × 10^5) + (4.5 × 10^4): convert the second to 0.45 × 10^5, then add: (3.2 + 0.45) × 10^5 = 3.65 × 10^5. Addition and subtraction are more involved than multiplication/division, so this calculator focuses on the latter.

What is the difference between scientific notation and engineering notation?

Scientific notation restricts the coefficient to [1, 10). Engineering notation restricts the exponent to multiples of 3 (corresponding to SI prefixes: kilo=10^3, mega=10^6, milli=10^−3, etc.), allowing coefficients from 1 to 999. Engineering notation is preferred in electronics and practical measurement because it aligns with unit prefixes.