Question 157692
To find the probability that {{{a/b}}} is less than 1 and can be expressed as a terminating decimal, simply list all of the fractions where {{{a<b}}} (since the fraction must be less than 1) and take note which ones have terminating decimals


{{{2/3=0.667}}} (non terminating), {{{2/4=1/2=0.5}}} (terminating), {{{2/5=0.4}}}, {{{2/6=0.333}}} (non terminating), {{{2/7=0.286}}}  (non terminating), etc...



It turns out that there are 3 different possible combinations of {{{a/b}}}. So count the number of terminating decimal fractions {{{a/b}}} and this will form the numerator while the total number of combintations (30) will form the denominator.



Let me know if you need more help.