Question

Find the value of (0.9)⁶, correct upto four places of decimal

Answer 1

(0.9)⁶ = (1 – 0.1)⁶

= ⁶C₀(1)⁶(0.1)⁰ – ⁶C₁(1)⁵(0.1)¹ + ⁶C₂(1)⁴(0.1)² – ⁶C₃(1)³(0.1)³ + ⁶C₄(1)²(0.1)⁴ – ⁶C₅(1)¹(0.1)⁵ + ⁶C₆(1)⁰(0.1)⁶

Since, ⁶C₀ = ⁶C₆ = 1, ⁶C₁ = ⁶C₅ = 6,

⁶C₂ = ⁶C₄ = ${\displaystyle \frac{6\times 5}{2\times 1}}$ = 15, ⁶C₃ = ${\displaystyle \frac{6\times 5\times 4}{3\times 2\times 1}}$ = 20 

∴ (0.9)⁶ = 1(1)(1) – 6(1)(0.1) + 15(1)(0.01) – 20(1)(0.001) + 15(1)(0.0001) – 6(1)(0.00001) + 1(1)(0.000001)

= 1 – 0.6 + 0.15 – 0.02 + 0.0015 – 0.00006 + 0.000001

= 0.531441

= 0.5314, correct upto 4 decimal places.