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16 May 2026, 10:40
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Difficulty:
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77% (02:19) correct
23%
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What is the sum of the first 50 digits after the decimal point in the decimal expansion of \( \frac17=0.142... \) ?
A) 200
B) 216
C) 219
D) 221
E) 227
A) 200
B) 216
C) 219
D) 221
E) 227
ankushsambare
Joined: 13 Jun 2022
Last visit: 02 Sep 2026
Posts: 311
Given Kudos: 227
Location: India
Schools: ISB '27 Wharton '26 INSEAD Aug '26
GPA: 2.4
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16 May 2026, 22:20
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The decimal expansion of 1/7 is:
1/7 = 0.142857142857...
The repeating block is:
142857
Sum of digits in one block:
1 + 4 + 2 + 8 + 5 + 7 = 27
The block has 6 digits.
We need the sum of the first 50 digits after the decimal point.
50 ÷ 6 = 8 remainder 2
So there are:
8 × 27 = 216
Next 2 digits are:
1 and 4
Their sum:
1 + 4 = 5
Total sum:
216 + 5 = 221
Answer: 221 (Choice D)
1/7 = 0.142857142857...
The repeating block is:
142857
Sum of digits in one block:
1 + 4 + 2 + 8 + 5 + 7 = 27
The block has 6 digits.
We need the sum of the first 50 digits after the decimal point.
50 ÷ 6 = 8 remainder 2
So there are:
- 8 complete blocks
- first 2 digits of the next block
8 × 27 = 216
Next 2 digits are:
1 and 4
Their sum:
1 + 4 = 5
Total sum:
216 + 5 = 221
Answer: 221 (Choice D)
17 May 2026, 02:50
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Thank you for the detailed explanation, but I have one question: how is someone supposed to know that 1/7 = 0.142857142857... without the use of the calculator? I mean, in this question it was 1/7, but it could have been any fraction, and it doesn't make sense to just memorize them randomly.
ankushsambare
