Answer: 1
Step-by-step explanation:
If we divide 4 by 37 we have:
[tex]\frac{4}{37}=0.108108108108108108[/tex] ...and more [tex]108[/tex] again and again...
This means that after the decimal point there are three digits (1, 0 and 8) that repeat infinitely. In addition, let's note the following:
[tex]8[/tex] is in the 3rd position after the decimal point, then it repeats in the 6th, then in the 9th, then in the 12nd...and so on.
Can you see the pattern?
[tex]8[/tex] is present in positions that are divisible by [tex]3[/tex]. So, we have to find the closest position to 100th that is multiple of [tex]3[/tex]:
It is the 99th position
Hence the 99th digit is also [tex]8[/tex] and the next digit (the 100th) is [tex]1[/tex].
