Answer:
The 100th digit to the right of the decimal point in the decimal form of 4/37 = 1
Step-by-step explanation:
Compute
[tex]\dfrac{4}{37} = 0.108108108108\dots\\\\= 0. \overline{108}[/tex]
This means the block of 3 digits 108 repeats an infinite number of times. This is known as a recurring decimal and the group of three digits 108 is known as a recurring group.
Since each recurring group is 3 digits, we observe that there are 100/3 = 33 repetitions of 108 in 100 digits
Therefore the total number of digits comprising 108 is 99 when we consider 100 places to the right:
0.108108.....0.108
The next digit which is the 100th digit is therefore 1