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Find the value of (0.9)6, correct upto four places of decimal - Mathematics and Statistics

Sum

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

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Solution

(0.9)6 = (1 – 0.1)6

= 6C0(1)6(0.1)06C1(1)5(0.1)1 + 6C2(1)4(0.1)26C3(1)3(0.1)3 + 6C4(1)2(0.1)46C5(1)1(0.1)5 + 6C6(1)0(0.1)6

Since, 6C0 = 6C6 = 1, 6C1 = 6C5 = 6,

6C2 = 6C4 = `(6 xx 5)/(2 xx 1)` = 15, 6C3 = `(6 xx 5 xx 4)/( 3 xx 2 xx 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.

Concept: Binomial Theorem for Positive Integral Index
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Exercise 4.2 | Q 10 | Page 77
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