# Uncertainty When Multiplying by $\pi$

When multiplying a number with an uncertainty by $\pi$, does the certainty differ, and if so, how?

Example:

$a = 10$

$\delta a = 1$

What is the uncertainty of $b$ where $b=\pi a$?

$$b = \pi(a)\;\; \implies\;\; b \;= \;10\pi\pm 1\cdot \pi \;= \;10\pi \pm \pi$$

$$\implies\;\; \delta b \;\;= \;\;\pi \;\;= \;\;\pi(\delta a)$$