Converting the given fractions into decimal form, we have,8/9 = 0.8818/23 = 0.7816/21 = 0.7614/17 = 0.82From the above, 0.88 is the largest.Corresponding fraction is 8/9.

Given expression=[(0.96)³ - (0.1)³] / [(0.96)² + (0.96 x 0.1) + (0.1)²]= [(a³ - b³) / (a² + ab + b²)] = (a - b)= (0.96 - 0.1)= 0.86

Given expression [(0.3333)/(0.2222)] x [((0.1667)(0.8333)) / ((0.6667)(0.1250))]=[(3333 / 2222)] x [((1/6) x (5/6)) / ((2/3) x (125/1000))]=[(3/2) x (1/6) x (5/6) x (3/2) x 8]=5 / 2=2.50

Given expression=[(0.1)³ + (0.02)³] / 2³ [(0.1)³ + (0.02)³]=1/8= 0.125

29.94 / 1.45 = 299.4 / 14.5 = [(2994 /14.5) x (1 / 10)] [ Here, Substitute 172 in the place of 2994/14.5 ]=172 / 10= 17.2

Let .009 / x = .01;   Then x = .009 / .01=.9 / 1= .9

Given expression = (11.98)² + (0.02)² + 11.98 x x.For the given expression to be a perfect square, we must have11.98 x x = 2 x 11.98 x 0.02 or x   = 0.04

Let 3889 + 12.952 - x = 3854.002.Then x = (3889 + 12.952) - 3854.002  = 3901.952 - 3854.002  = 47.95.

144 / 0.144 = 14.4 / x144 x 1000 / 144 = 14.4 / x  x =14.4 / 1000 = 0.0144

3/4 = 0.75,  5/6= 0.833,  1/2= 0.5,   2/3= 0.66,4/5= 0.8,   9/10= 0.9. Clearly, 0.8 lies between 0.75 and 0.833.4/5 lies between 3/4 and 5/6.