[(0.87) ³ + (0.13) ³] / [(0.87) ² - 0.87 x 0.13 + (0.13) ²] =?

Given Expression = (1.04)² + 1.04 x 0.04 + (0.04)² / (1.04)³ - (0.04)³
= (a² + ab + b²) / (a³ - b³)
= (a² + ab + b²) / [(a-b) (a² + ab + b²)]
= 1 / (a - b)
= 1/ (1.04 - 0.04)
= 1

Given expression
= [(0.47)³ - (0.33)³] / [(0.47)² + 0.47 x 0.33 + (0.33)²]
= [a³ - b³ ] / [ a² + ab + b²]
= [(a-b) (a² + ab + b²)] / [(a² + ab + b²)]
= (a - b)
= (0.47 - 0.33)
= 0.14

Given expression
= [(0.5)³ + (0.3)³] / [(0.5)² - 0.5 x 0.3 + (0.3)²]
= [a³ + b³] / [a² - ab + b²]
= [(a + b)(a² - ab + b²)] / [a² -ab + b²]
= a+b
= 0.5 + 0.3
= 0.8

Given expression
= [(0.5)³ + (0.6)³ ] / [(0.5)² - 0.5 x 0.6 + (0.6)²]
= (a³+b³) / ( a²-ab+b²)
= a + b
= 0.5 + 0.6
= 1.1

Given expression
=[(3.65)² + (2.35)² -2 x 3.65 x 2.35 ] / 1.69
=a² + b² - 2ab / 1.69, Where a = 3.65 and b = 2.35
=(a - b)² / 1.69
= (3.65 - 2.35)² / 1.69
= (1.3)² / 1.69
= 1.69 / 1.69
= 1

Given expression = 3 / [ 3+ {(0.3 - 3.03) / (3 x 0.91)}]
= 3 / [3- { 273 / (3 x 91)}]
= 3 / (3-1)
= 3 / 2
= 1.5

Given expression = (0.01 - 0.0001) / (0.00001 + 1)
= (.0099 / .0001) + 1
= 99 + 1
= 100

The given number are 3.00, 0.09 and 2.70
LCM = LCM of numerator / HCF of denominator
L. C. M of 300, 9 and 270 is 2700
? Required L.C.M = 27.00 = 27

The Given Number are 1.08, .36 and 0.9
G. C. D of 108, 36 and 90 is 18
? Required G. C. D. = 0.18

= 0.136
= (136 - 1) / 990
= 135 / 990
= 3 / 22