The rule
n = m × 10ᵉ, with 1 ≤ |m| < 10
Why it works
Scientific notation writes any number as a single digit, some decimals, and a power of ten. It exists because 0.000000000000000000000000001673 is unreadable and 1.673 × 10⁻²⁷ is not, and because the exponent alone tells you the scale.
How to do it by hand
- Move the decimal point until one non-zero digit is to its left
- Count how many places it moved
- Moving left gives a positive exponent, moving right a negative one
- For engineering notation, adjust so the exponent is a multiple of three
What is worth knowing
The real value is not brevity but significant figures. Writing 1500 leaves it ambiguous whether you measured to the nearest hundred or the nearest unit; 1.5 × 10³ and 1.500 × 10³ say exactly which. That precision is why every scientific field uses it. Engineering notation exists for a different reason: keeping the exponent a multiple of three lines it up with kilo, mega, giga, milli and micro, so 4.7 × 10⁻³ farads reads directly as 4.7 millifarads.