Problem: If (1.0025)10 is evaluated correct to 5 decimal places, then the digit in the fifth decimal place is
Answer Choices:
A. 0
B. 1
C. 2
D. 5
E. 8
Solution:
The binomial expansion gives (1.0025)10=(1+.0025)10=1+10(.0025)+ 45(.0025)2+120(.0025)3+210(.0025)4+…=1.025+.00028125+ .000001875+ terms less than 10−8=1.02528 accurate to 5 decimal places.