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- MorningfoxLv 74 weeks ago
Lets use x = a/b. Then we have 10000x = 16(1/x). So then 10000x^2 = 16. That means that x^2 = 16 /10000, or x = +/- 4/100 = +/- 0.04 = +/- 1/25. Since 0.abcdefg... doesn't have a minus sign, the answer is a/b = 1/25.

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- billrussell42Lv 74 weeks ago
α/β = 0.abcdefg...

10000α/β = abcd.efg... = 16β/α

10000α/β = 16β/α

10000(α/β)² = 16

(α/β)² = 16/10000

α/β = 4/100 = 1/25

check

α/β = 1/25 = 0.040000

16β/α = 16•25 = 400.000

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