Question

using Binomial theorem Evaluate (0.98) to the power -3 upto four decimal places

Answer 1

(9.8)⁻³ = (10 - 0.2)⁻³ = 10⁻³(1 - 0.2/10)⁻³ = 0.001(1 - 0.02)⁻³
Now , according to binomial expansion
(1 + y)ⁿ = (1+ ny) , when 1 >>y

Here , 10 >> 0.2
so, 0.001{1 - (0.02)(-3)}
= 0.001 × (1 + 0.06)
= 0.001 × 1.06
= 0.00106

Hence , (9.8)⁻³ = 0.0010 upto 4 decimal place