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Question
Using binomial theorem, find the value of (9.9)3
Solution
(9.9)3 = (10 – 0.1)3
= 3C0 (10)3 (0.1)0 – 3C1 (10)2 (0.1)1 + 3C2 (10)1 (0.1)2 – 3C3 (10)0 (0.1)3
Since, 3C0 = 3C3 = 1, 3C1 = 3C2 = 3
∴ (9.9)3 = 1(1000)(1) – 3(100)(0.1) + 3(10)(0.01) – 1(1)(0.001)
= 1000 – 30 + 0.3 – 0.001
= 1000.3 – 30.001
= 970.299
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