When using linear interpolation, with similar triangles, to find the root of a function you narrow down the interval the root is in.
If $f(1) < 0$ and $f(2) > 0$ then the root is in $[1, 2]$
Then you do linear interpolation to find $1.460, f(1.460) < 0$, then the root is in $[1.460, 2]$
Then again linear interpolation is done to find $1.467$, say $f(1.467) < 0$, so the root is in $[1.467, 2]$
Why is it that you stop and find the answer because $1.460 = 1.467$ (to 1 dp)? (ie the last two attempts are equal when rounded to 1 dp)
Why don't you stop when in the interval $[a, b], a = b$ when $a$ and $b$ are rounded to $1$ d.p.?