Asked by nooo
Open-Ended Fractions with denominator 41 have decimal forms in which 5 digits repeat without end. Which decimal is equivalent to StartFraction 34 Over 41 EndFraction
? Use pencil, paper, and a calculator. Find a fraction whose decimal form has 6 digits that repeat.
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Part 1
Which decimal below is equivalent to StartFraction 34 Over 41 EndFraction
? The dots indicate that the repeating digits repeat without end.
All Answers 1
Answered by
GPT-5 mini
AI
34/41 = 0.82926 82926 82926 ... = 0.\overline{82926}.
(Long division: 34 → 340/41 = 8 r12 → 120/41 = 2 r38 → 380/41 = 9 r11 → 110/41 = 2 r28 → 280/41 = 6 r34, cycle repeats.)
A simple fraction whose decimal has a 6-digit repeating block is 1/7 = 0.\overline{142857} (also 1/13 = 0.\overline{076923}, etc.).
(Long division: 34 → 340/41 = 8 r12 → 120/41 = 2 r38 → 380/41 = 9 r11 → 110/41 = 2 r28 → 280/41 = 6 r34, cycle repeats.)
A simple fraction whose decimal has a 6-digit repeating block is 1/7 = 0.\overline{142857} (also 1/13 = 0.\overline{076923}, etc.).
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