VeritasPrepKarishma wrote:
aj0809 wrote:
Hi,
The question stem sounds way too difficult for me to comprehend. Can someone kindly explain what the question asking us to find?
Thanks
Look at the question one sentence at a time:
"The decimal d is formed by writing in succession all the positive integers in increasing order after the decimal point; "
This is how decimal d is formed - write all positive integers (i.e. 1, 2, 3, etc) in increasing order
"that is d = 0.123456789101112"
Here they have shown what they mean
d = 0.123456789
101112... and so on goes the decimal
"What is the 100th digit of d to the right of decimal point ?"
If you continue putting down positive integers in increasing order, you will get a decimal with infinite digits to the right of decimal. What will be the 100th digit?
d = 0.1234567891011121314...
first digit after decimal is 1
second digit is 2
third digit is 3
10th digit is 1
What will be 100th digit?
First 9 digit will be 1 to 9.
Next 90 digits will come from the next 45 two digit numbers. The next 45 two digit numbers are 10 - 54.
We have accounted for 99 digits. The 100th digit will be the 5 of 55.
Using your reasoning above I just wanted to check if this would be the right approach if the question asked for the 200th digit to the right of the decimal.
First 9 digits is 1 to 9
The next 191 digits will come from a combination of two digit and three digit numbers because we do not have enough two digit integers to reach 200 digits.
So we have to find how many digits we need to get to the 99th two digit integer. From 10 - 99 is 90 two digit integers which is 180 digits therefore next 180 digits will come from the next 90 two digit numbers which are 10 - 99.
We now have 9 + 180 = 189 digits but we still need 11 to get to the 200th digit.
Because the next batch of numbers are 3 digit numbers we need to take the next 3 (11/3) three digit numbers with are 100, 101, 102 with a remainder of 2 1(
0)3. Therefore 0 is the 200th digit.