2011 digits
Weekly Problem 10 - 2014
What is the sum of the first $2011$ digits when $20 \div 11$ is written as a decimal?
Age
14 to 16
Challenge level
Problem
What is the sum of the first 2011 digits when 20 รท 11 is written as a decimal?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 9046
Image
First 2011 digits of 1.818181...
Each pair adds up to 9
There are 2011$\div$2 = 1005 remainder 1 pairs
Sum = 1005$\times$9 + 1 (from ...18...)
= 9046