Scientific Notation and Significant Figures

Scientific notation expresses numbers as a × 10^b, where a is between 1 and 10 and b is an integer. This makes it much easier to work with extremely large or extremely small numbers that appear constantly in science and engineering.

Examples

The speed of light is about 3 × 10⁸ m/s. The mass of an electron is about 9.109 × 10⁻³¹ kg. Writing these out in full (300,000,000 and 0.0000000000000000000000000000009109) is impractical and error-prone.

Significant Figures

Significant figures indicate the precision of a measurement. Non-zero digits are always significant. Zeros between non-zero digits are significant. Leading zeros are not significant. Trailing zeros after a decimal point are significant. When multiplying or dividing, the result should have the same number of significant figures as the least precise measurement.

Arithmetic with Scientific Notation

When multiplying, multiply the coefficients and add the exponents: (3 × 10⁴)(2 × 10³) = 6 × 10⁷. When dividing, divide the coefficients and subtract the exponents. When adding or subtracting, first convert to the same exponent, then add or subtract the coefficients.

For mathematical computations of all types, try our Scientific Calculator.