UPSC NDA I 2015 Mathematics Solved Paper

Consider the whole number 127. Hence it can be converted into Binary into following steps
127
i)‌127=2(63)+1→1
ii)‌63=2(31)+1→1
iii)‌31=2(15)+1→1
iv)‌15=2(7)+1→1
v)‌7=2(3)+1→1
vi)‌3=2(1)+1→1
vii)‌1=2(0)+1→1
(127)10→(1111111)2
Hence, the binary of 127 is seven times 1 or (1111111).
Now for the binary of the number after the point, we get
0.25×2=0.5→0
0.5×2=1.0→1
∴(0.25)10=(.01)2
∴(127.25)−10=(1111111.01)2