- The leftmost non-zero digit is the **most significant digit**.
- If there is no decimal point, the rightmost non-zero digit is the **least significant digit**.
- Otherwise, the right-most digit (including zeroes) is the least significant digit.
- All digits between the most and least significant digits are significant.
- Pure (discrete) numbers are unitless and have infinite significant figures.
!!! example
In $123000$, there are 3 significant digits.<br>
In $0.1230$, there are 4 significant digits.
- When adding or subtracting significant figures, the answer has the **same number of decimals** as the number with the lowest number of decimal points.
- When multiplying or dividing significant figures, the answer has the **same number of significant figures** as the number with the lowest number of significant figures.
- Values of a calculated result can be **no more precise** than the least precise value used.
When rounding an answer with significant figures, if the **least significant figure** is $5$, round up only if the **second-least** significant figure is odd.
$$1.25 + 1.2 = 2.4$$
$$1.35 + 1.2 = 2.6$$
### Scientific notation
Scientific notation is written in the form of $m×10^{n}$, where $1 \leq m <10,n \in \mathbb{Z}$.Alldigitsbeforethemultiplicationsigninscientificnotationaresignificant.<br>
!!! example
The speed of light is 300 000 000 ms<sup>-1</sup>, or $3×10^8$ ms<sup>-1</sup>.
### Orders of magnitude
The order of magnitude of a number can be found by converting it to scientific notation and taking its power of 10.
!!! example
- The order of magnitude of 212000, or $2.12×10^{5}$, is 5.
- The order of magnitude of 0.212, or $2.12×10^{-1}$, is -1.
