In the decimal expansion of the raional number 3/7, what is the 2006th digit after the decimal point? Please explain your reasoning so I can understand :)
2007-01-28 22:17:31 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
3/7 = 0.428571429. . . . .the deimal is non terminating non repeating and goes on to infinity
2-006 / 6 = 334. 33333333. . .this decimal is non terminating, repeating and go on to infinity
-- - - - - - - - -s-
2007-01-29 00:57:37 · answer #1 · answered by SAMUEL D 7 · 0⤊ 0⤋
If you divide 3 by 7 you get
0.428571428571.... (the "428571" part is recurring)
the 1st digit after the decimal point is 4, so is every 6th further digit, ie 7th, 13th, 19th digit after the decimal point is 4
To get what the 9th digit is, divide the 9 by 6: you get 1 remainder 3. The remainder is the important bit... so take the 3rd digit of the recurring part, "428571" - so the 9th digit is "8"
Similarly, to get the 2006th digit, divide 2006 by 6, you get 334 (and a remainder of 2)... the second digit of the recurring part is 2, so the 2006th digit after the decimal point is 2.
2007-01-29 06:30:16 · answer #2 · answered by tank 2 · 0⤊ 0⤋
3/7 is equivalent of 0.428571...recurring.
In other words, "428571" repeat without ending.
In the 2006th decimal place, the number is "2" because when you divide 2006 by 6 (number of digits of "428571", there are 334 repetitions and two more digits to fill. Therefore, the 2006th digit should be the second number of the repeating sequence, which is 2. I hope that helps :D
2007-01-29 06:31:24 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Simple. 30/7 is a recurring decimal which means that after a certain no of digits the decimal value repeats itself endlessly.
30/7= 0.428571428571428571................
in this case the decimal reccurs after 6 digits.
therefore 2006/6= 334 remainder:2
the 2006 th digit is (2).
2007-01-29 06:34:16 · answer #4 · answered by pro man 1 · 0⤊ 0⤋
If you make the division you´ll find out that there is a group of six numbers 428571 repeting periodically.
So dividing 2006 into 6 you get 334 and a remainder of of 2
So there are 334 entire groups of six and two figures of the following group
The figure is 2
2007-01-29 06:34:18 · answer #5 · answered by santmann2002 7 · 0⤊ 0⤋
3/7=0.42857142857142857142857...
The 6th digit is 1
The 12th digit is 1 too. 12=6*2
The 18th digit is 1 too. 18=6*3
...
The 2004th digit is 1 too because 2004=6*334
The 2005th digit is 4
The 2006th digit is 2
2007-01-29 06:36:44 · answer #6 · answered by Serban 2 · 0⤊ 0⤋