We can rewrite #0.35# as #35/100#.

Then we can rewrite this expression as:

#(8/15)/(35/100)#

We can now use this rule for dividing fractions to calculate the value of the expression:

#(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))#

#(color(red)(8)/color(blue)(15))/(color(green)(35)/color(purple)(100)) = (color(red)(8) xx color(purple)(100))/(color(blue)(15) xx color(green)(35)) = 800/525 = (25 xx 32)/(25 xx 21) = (color(red)(cancel(color(black)(25))) xx 32)/(color(red)(cancel(color(black)(25))) xx 21) = 32/21#

Or

#1.524# rounded to the nearest thousandth