Question

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

Answer 1

The value is 0.531441
But according to question the answer is 0.5314

Answer 2

Solution :

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By Binomial Theorem :

$\rm \displaystyle \left ( x + a )^n = ^nC_{0}x^{n}+^nC_{1}x^{n-1}a^{r}+..+ ^nC_{r}x^{n-r}a^{r}+...+^nC_{n}a^{n} \right )$

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Here ,

$ ( 0.9 )^6 $

= $ ( 1 - 0.1 )^6 $

= $\rm \displaystyle{ ( 1 - 0.1 )^6 = ^6C_{0}x^{6}+^6C_{1}1^{5-1}(0.1)^{1}-^6C_{2}(0.1)^2+^{6}C_{3}(0.1)^{3}-^{6}C_{4}(0.1)^4+^{6}C_{5}(0.1)^{5}+^{6}C_{6}(0.1)^{6} }$

= $\rm \textsf { 1 - 6×(0.1) + 15 × (0.1)^2-20(0.1)^3+15(0.1)^4-6(0.1)^5-(0.1)^6 }$

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

= 1.151501 - 0.620060

= 0.531441

≈ 0.5314

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