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Sunday, April 7, 2013

Binomial Theorem

Category: Algebra, Arithmetic

"Published in Newark, California, USA"

Evaluate 



without using a calculator.

Solution:

Consider the given number



Rewrite and expand the given number as follows



It is better to convert the decimal number into its equivalent fraction for the given number 



Next, use the Binomial Theorem to expand the given number as follows











Get the Least Common Denominator (LCD) for all the fractions and simplify as follows







Convert the fraction into its equivalent decimal number as follows



Therefore,



Check:

If you will use a scientific calculator,



which is almost the same as the final answer.