I am trying to compute the rounding error bounds for 3.4*0.43 in $\mathbb{F}_{10}(2)$ where $\mathbb{F}_{B}(t) = \{x=\pm \sum_{j=1}^t c_jB^{-j+e}|e\in \mathbb{Z},c_j \in \mathbb{Z_B},c_1 \neq 0\} \cup \{0\} $ , $ x\in \mathbb{F}_{B}(t)$, $\mathbb{Z_B}$ = $\{0,…,B−1\}$ (the digits) and B is the basis.
But I can't remember how to do this?
Could someone please help me understand how to solve this question?
Your numbers have 2 significant digits. Thus they both represent intervals, $[3.35,3.45]$ and $[0.425,0.435]$. Which end-point actually belongs to the interval depends on the rounding mode. The true numbers behind the floating point representation could be any numbers in these intervals. Thus the true product could be anything in $[1.42375, 1.50075]$ while the floating point result is $1.5$, rounded from $1.462$. From that you can read off what errors are possible.