Question

Evaluate 0.985 using the Binomial Theorem. Write 0.98 as a binomial: (1 + _______)

Answer 1

Answer:

The value of $0.98^5$ is 0.9039207968.

Step-by-step explanation:

We need to find the value of $0.98^5$.

According to the binomial theorem,

$(a+b)^n=^nC_0a^n+^nC_{1}a^{n-1}b+...+^nC_{n-1}a^1b^{n-1}+^nC_nb^n$

Write 0.98 as a binomial: (1 - 0.02)

Write 0.98 as a binomial: (1 + (-0.02))

$0.98^5=(1 + (-0.02))^5$

Using binomial theorem, we get

$0.98^5=^5C_0(1)^5+^5C_1(1)^4(-0.02)^1+^5C_2(1)^3(-0.02)^2+^5C_3(1)^2(-0.02)^3+^5C_4(1)^1(-0.02)^4+^5C_5(1)^0(-0.02)^5$

$0.98^5=(1)+5(-0.02)^1+10(-0.02)^2+10(-0.02)^3+5(-0.02)^4 +1(-0.02)^5$

$0.98^5=(1)+(-0.1)+(0.004)+(-0.00008)+0.0000008+(-0.0000000032)$

$0.98^5=0.9039207968$

Therefore the value of $0.98^5$ is 0.9039207968.

Answer 2

Evaluate 098^5 using the binomial theorem 

-0.02