Given Expression =$\dfrac{a^2- b^2}{a - b} $=$ \dfrac{(a + b)(a - b)}{(a - b)} $= a + b = 2.39 + 1.61 = 4.
Required decimal =$ \dfrac{1}{60 \times 60} $=$ \dfrac{1}{3600} $= .00027
Given expression
=$ \dfrac{(0.96)^3- (0.1)^3}{(0.96)^2+ (0.96 \times 0.1) + (0.1)^2} $
= $ \left(\dfrac{a^3- b^3}{a^2 + ab + b^2} \right) $
= $\left( a - b \right)$= (0.96 - 0.1)= 0.86
Given Expression = $\dfrac{(0.1)^3+(0.02)^3}{2^3[(0.1)^3+(0.02)^3]}$ = $ \dfrac{1}{8}$= 0.125
=$\dfrac{29.94}{1.45}$=$\dfrac{299.4}{14.5}$
=$\left(\dfrac{2994}{14.5}\times\dfrac{1}{10}\right)$[ Here, Substitute 172 in the place of 2994/14.5 ]
=$\dfrac{172}{10}$
=17.2
6.$\overline{46}$ = 6 + 0.$\overline{46}$ = 6 +$ \dfrac{46}{99} $ =$ \dfrac{594 + 46}{99} $ =$ \dfrac{640}{99} $.
101$ \dfrac{27}{100000} $= 101 +$ \dfrac{27}{100000} $= 101 + .00027 = 101.00027
$ \dfrac{0.0203 \times 2.92}{0.0073 \times 14.5 \times 0.7} $=$ \dfrac{203 \times 292}{73 \times 145 \times 7} $=$ \dfrac{4}{5} $= 0.8
$\dfrac{4.036}{0.04}$=$ \dfrac{403.6}{4} $= 100.9
3.87 - 2.59 = 3 + 0.87 - 2 + 0.59
=$ \left(3 +\dfrac{87}{99} \right) $-$ \left(2 +\dfrac{59}{99} \right) $
= 1 +$ \left(\dfrac{87}{99} -\dfrac{59}{99} \right) $
= 1 +$ \dfrac{28}{99} $
= 1.28.