Step by step
The question
Question: What is the 33rd digit after the decimal point of 4/11?
1 Find the block
40 divided by 11 is 3, and 7 is left.
We divide 4 by 11 the long way.
Each time we bring down a 0.
70 divided by 11 is 6, and 4 is left.
4 left: that is where we started.
So the digits repeat from here.
So 4/11 is 0 point 3 6, and the same 2 digits again and again.
The block is 2 long.
2 Divide
The block comes again and again.
So we divide by its length.
What is left over tells us the place in the block.
2 times 16 is 32.
So 16 full blocks take us to the 32nd digit.
33 minus 32 is 1 more.
3 Count into the block
Careful!
The 16 only counts full blocks.
The 1 left over gives the place.
1 left means place 1 in the block: 3.
4 Check
Let's check by counting on.
A block ends at the 32nd digit.
Then we count on: 3.
The 33rd is 3.
So it is right!
Let's look back.
First: find the block.
Then: divide.
Then: count into the block.
Last: check.