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In the repeating decimal 0.0653906539..., the 34th digit to
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24 May 2017, 02:00
24 May 2017, 02:00
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Question Stats:
82% (00:35) correct
17% (00:32) wrong based on 140 sessions
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In the repeating decimal 0.0653906539..., the 34th digit to the right of the decimal point is
A) 9
B) 6
C) 5
D) 3
E) 0
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Joined: 10 Apr 2015
Posts: 6218
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Re: In the repeating decimal 0.0653906539..., the 34th digit to
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06 Jun 2017, 16:05
06 Jun 2017, 16:05
2
Carcass wrote:
In the repeating decimal 0.0653906539..., the 34th digit to the right of the decimal point is
A) 9
B) 6
C) 5
D) 3
E) 0
Given: 0.0653906539
1st digit: 0
2nd digit: 6
3rd digit: 5
4th digit: 3
5th digit: 9
6th digit: 0
7th digit: 6
8th digit: 5
9th digit: 3
10th digit: 9
11th digit: 0
12th digit: 6
Notice that the pattern repeats itself every 5 digits.
So, the 5th decimal is 9, the 10th decimal is 9, the 15th decimal is 9, the 20th decimal is 9,...
The 34th digit to the right of the decimal point is
We know that the 30th decimal is 9
Which means the 31th decimal is 0, the 32nd decimal is 6, the 33rd decimal is 5, the 34th decimal is 3
Answer:
Show: ::
D
Cheers,
Brent
Re: In the repeating decimal 0.0653906539..., the 34th digit to
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20 Aug 2019, 06:58
20 Aug 2019, 06:58
1
Here is how I like to do these problems
1) identify how many numbers are in the pattern before it repeats
5 in this case (06539)
2) divide the desired digit by the number of numbers in the pattern
in this case \(\frac{34}{5}\)
3) our result is \(6\frac{4}{5}\)
4) This means at the 34th digit we have completed 6 complete patterns (or repeating sequences) and 4 fifths of one more pattern.
. the 4th number out of 5 is 3, as can be seen here: 06539
. Or here is another way to look at it. You can see at the 34th digit we have completed 6 full patterns and 4/5ths of the next one
06539 06539 06539 06539 06539 06539 0653
. the answer is 3
5) you obviously don't have to write the first 6 complete patterns. Just write out one complete pattern and advance to that fraction you have found. So, our fraction was 4/5ths so we move to the 4th out of 5th value of 06539. Which is 3.
1) identify how many numbers are in the pattern before it repeats
5 in this case (06539)
2) divide the desired digit by the number of numbers in the pattern
in this case \(\frac{34}{5}\)
3) our result is \(6\frac{4}{5}\)
4) This means at the 34th digit we have completed 6 complete patterns (or repeating sequences) and 4 fifths of one more pattern.
. the 4th number out of 5 is 3, as can be seen here: 06539
. Or here is another way to look at it. You can see at the 34th digit we have completed 6 full patterns and 4/5ths of the next one
06539 06539 06539 06539 06539 06539 0653
. the answer is 3
5) you obviously don't have to write the first 6 complete patterns. Just write out one complete pattern and advance to that fraction you have found. So, our fraction was 4/5ths so we move to the 4th out of 5th value of 06539. Which is 3.
