SL 1.1—Scientific notation

Scientific notation writes a non-zero number as a × 10ⁿ, where 1 ≤ |a| < 10. The coefficient carries the significant digits; the integer exponent records how far the decimal point has moved and therefore the scale of the quantity.

To convert 0.00042, move the decimal point four places right to obtain 4.2, so 0.00042 = 4.2 × 10⁻⁴. For multiplication, multiply coefficients and add exponents: (3 × 10⁵)(2 × 10⁻³) = 6 × 10². For addition or subtraction, first rewrite the terms with the same power of ten.

The exponent is not the number of significant figures. A negative exponent describes a number between 0 and 1, and a coefficient such as 42 is not normalized scientific notation because its magnitude is greater than 10.

IB written-form boundary: calculator notation such as 5.2E30 is not acceptable in a final answer; write $5.2\times10^{30}$. After multiplying or dividing, renormalize the coefficient so its magnitude is at least 1 and less than 10. For example, $24\times10^7=2.4\times10^8$.