Step by step
The question
Question: What is the 25th digit after the decimal point of 1/37?
1 Find the block
10 divided by 37 is 0, and 10 is left.
We divide 1 by 37 the long way.
Each time we bring down a 0.
100 divided by 37 is 2, and 26 is left.
260 divided by 37 is 7, and 1 is left.
1 left: that is where we started.
So the digits repeat from here.
So 1/37 is 0 point 0 2 7, and the same 3 digits again and again.
The block is 3 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.
3 times 8 is 24.
So 8 full blocks take us to the 24th digit.
25 minus 24 is 1 more.
3 Count into the block
Careful!
The 8 only counts full blocks.
The 1 left over gives the place.
1 left means place 1 in the block: 0.
4 Check
Let's check by counting on.
A block ends at the 24th digit.
Then we count on: 0.
The 25th is 0.
So it is right!
Let's look back.
First: find the block.
Then: divide.
Then: count into the block.
Last: check.