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Updated on: 17 Jun 2022, 01:49
Originally posted by violetsplash on 24 Sep 2013, 08:35.
Last edited by Bunuel on 17 Jun 2022, 01:49, edited 2 times in total.
Last edited by Bunuel on 17 Jun 2022, 01:49, edited 2 times in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
72% (01:59) correct
28%
(01:50)
wrong
based on 2035
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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
What is the 100th digit of d to the right of decimal point ?
A. 0
B. 1
C. 5
D. 8
E. 9
I got the answer of this question after writing the 100th term in the series - although it was correct but it was time consuming. Not able to figure out the pattern. Can someone please help ?
24 Sep 2013, 08:47
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Here is comparatively simpler way....
The number is 0.123456789101112.........
After Decimal digit
1 - 9 -------------------- 9 Digits
10 - 19 ----------------- 20 digits
20 - 29 ----------------- 20 digits
30 - 39 ----------------- 20 digits
40 - 49 ----------------- 20 digits
50 - 54 ----------------- 10 digit
5 and 4 are the 98th and 99th digits respectively hence 100th will be 5
Alternate Approach
Assume there are 100 blank spaces to fill.
First 9 places will be filled by first 9 single digit numbers i.e. 1 to 9.
We are now left with 91 places which will be filled by 2 digit numbers starting from 10.
TO fill 91 places we would need 91/2 = 45 numbers starting from 10. which will end on the number 54. Next number, for filling out 91th place, will be 5 from (55).
Hope that helps!
Narenn
The number is 0.123456789101112.........
After Decimal digit
1 - 9 -------------------- 9 Digits
10 - 19 ----------------- 20 digits
20 - 29 ----------------- 20 digits
30 - 39 ----------------- 20 digits
40 - 49 ----------------- 20 digits
50 - 54 ----------------- 10 digit
5 and 4 are the 98th and 99th digits respectively hence 100th will be 5
Alternate Approach
Assume there are 100 blank spaces to fill.
First 9 places will be filled by first 9 single digit numbers i.e. 1 to 9.
We are now left with 91 places which will be filled by 2 digit numbers starting from 10.
TO fill 91 places we would need 91/2 = 45 numbers starting from 10. which will end on the number 54. Next number, for filling out 91th place, will be 5 from (55).
Hope that helps!
Narenn
03 Dec 2014, 20:17
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aj0809
Hi,
The question stem sounds way too difficult for me to comprehend. Can someone kindly explain what the question asking us to find?
Thanks
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 = 0.123456789101112... 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.
