abhasjha wrote:The decimal d is formed by writing in succession all the positive integers in increasing order after the decimal point; that is d = 0.123456789101112

What is the 100th digit of d to the right of decimal point ?

a) 0
b) 1
c) 5
d) 8
e) 9

Since we need to determine the 100th digit, proceed as follows:
Write out the first 100 integers, digit by digit, so that there are 10 DIGITS PER ROW.
LOOK FOR A PATTERN.

1-2-3-4-5-6-7-8-9-1
0-1-1-1-2-1-3-1-4-1
5-1-6-1-7-1-8-1-9-2
0-2-1-2-2-2-3-2-4-2

The digits in red imply the following pattern:
10th digit -->1
20th digit -->1
30th digit -->2
40th digit -->2
50th digit -->3
60th digit -->3
70th digit -->4
80th digit -->4
90th digit -->5
100th digit -->5

The correct answer is C.

abhasjha wrote:The decimal d is formed by writing in succession all the positive integers in increasing order after the decimal point; that is d = 0.123456789101112

What is the 100th digit of d to the right of decimal point ?

a) 0
b) 1
c) 5
d) 8
e) 9



any one having a quicker method than how i approached this problem ?

There are 9 Single-digit numbers:
.123456789
9 digits Counted, 91 remaining

Two-digit numbers:
With 91 remaining, we can handle 45 TWO-DIGIT NUMBERS (which will accommodate 90 of the required digits)

First 10 two digit numbers will have 1 on their tens place and 0 to 9 consecutively on their units place
Next 10 two digit numbers will have 2 on their tens place and 0 to 9 consecutively on their units place
Next 10 two digit numbers will have 3 on their tens place and 0 to 9 consecutively on their units place
Next 10 two digit numbers will have 4 on their tens place and 0 to 9 consecutively on their units place
now 6th Two digit number will have 5 at the tens place which will be the 91st Digit

Answer: Option C