Thank you for posting you question here at brainly. Below is the solution:
1/97 = 1 / (100-3) = 1 / (xo + dx)
so, you have now that
x = xo + dx, where x = 97, xo = 100, and dx = - 3. Recognizing that 3 << 100, we can write the Taylor expansion around xo
1/ (xo + dx) ~ 1/xo + d/dx(1/xo)dx = 1/xo + (-1/xo^2)dx
= 1/100 - (1/100^2) (-3) = 1/100 + 3/100^2
= 1/100 + 3/10000
= 0.01 + 0.0003
= 0.0103
