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The mass of an electron is 0.0000000000000000000000000000009109 kg0.0000000000000000000000000000009109\text{ kg}, while the Sun weighs about 1,989,000,000,000,000,000,000,000,000,000 kg1,989,000,000,000,000,000,000,000,000,000\text{ kg}.
Writing dozens of zeros in every physics calculation is not just tedious—it practically guarantees a transcription error.

Anatomy of Scientific Notation

Scientific notation is a standardized way to represent any real number as the product of a decimal and an integer power of ten: a×10na \times 10^n.
The coefficient aa must satisfy 1≤∣a∣<101 \le |a| < 10, meaning exactly one non-zero digit sits to the left of the decimal point.
The exponent nn is an integer that counts how many factors of ten scale that coefficient up or down.
In the 3rd century BCE, Archimedes laid the conceptual foundation for this in The Sand Reckoner, designing a base-10 counting system to estimate how many grains of sand could fill the entire cosmos.
How do we compress a massive number like the distance from Earth to the Sun into this exact format?

Converting Large Numbers

To convert a number greater than 1010, count how many places you must shift the decimal point to the left until only one non-zero digit remains.
Every leftward shift divides the coefficient by 1010, so you must multiply by 10+110^{+1} to keep the total physical value unchanged.