Scientific notation in simple words
Scientific notation is a short way to write very big or very small numbers. You write a number from 1 up to (but not including) 10, times 10 to a power.
The power says how many places the decimal point moved. For big numbers the power is positive; for tiny numbers it is negative.
For example, 123,456.789 becomes 1.23456789 × 10⁵, because the decimal point moved 5 places to the left. And 0.00045 becomes 4.5 × 10⁻⁴, because the point moved 4 places to the right.
Formula and method
Scientific notation moves the decimal so the nonzero coefficient has magnitude from 1 up to, but excluding, 10. The exponent records the movement.
Worked example
0.004560 becomes 4.560 × 10^−3. The written trailing zero is retained.
Arithmetic in scientific notation
To multiply, multiply the coefficients and add the exponents: (3.2 × 10⁵) × (4 × 10³) = 12.8 × 10⁸. The coefficient 12.8 is not between 1 and 10, so renormalize by moving the point one place left and raising the exponent by one: 1.28 × 10⁹.
To divide, divide the coefficients and subtract the exponents. To add or subtract, first rewrite both numbers with the same exponent: 3.2 × 10⁵ + 4 × 10³ = 3.2 × 10⁵ + 0.04 × 10⁵ = 3.24 × 10⁵.
E-notation and engineering notation
E-notation writes the power of ten after the letter e, so 4.5 × 10⁻⁴ is 4.5e-4. Calculators and spreadsheets use this form. Engineering notation restricts the exponent to multiples of three, matching SI prefixes: 0.00045 is 450 × 10⁻⁶, or 450 micro-units.