0.6777777777777777777777777777777777777777777777777777777777777777777777777777777777777777779999999999999999999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888888888888888888888888888888887777777777777777777777777777
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What is 0.67777777777777777777777777777777777777777777777777777777777777777777777777777777777777777799999999999999999999999999999999999999999999999999999999999999888888888888888888888888888888888888888888888888888888888888888888888888877777777777777777777777777777777777777777777777777777799999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888888888777777777777777777777777777777777777777777777777999999999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888877777777777777777777777777777777777777777777999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888888877777777777777777777777777777777777777777799999999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888877777777777777777777777777777 as a fraction?
To write 0.67777777777777777777777777777777777777777777777777777777777777777777777777777777777777777799999999999999999999999999999999999999999999999999999999999999888888888888888888888888888888888888888888888888888888888888888888888888877777777777777777777777777777777777777777777777777777799999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888888888777777777777777777777777777777777777777777777777999999999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888877777777777777777777777777777777777777777777999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888888877777777777777777777777777777777777777777799999999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888877777777777777777777777777777 as a fraction you have to write 0.67777777777777777777777777777777777777777777777777777777777777777777777777777777777777777799999999999999999999999999999999999999999999999999999999999999888888888888888888888888888888888888888888888888888888888888888888888888877777777777777777777777777777777777777777777777777777799999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888888888777777777777777777777777777777777777777777777777999999999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888877777777777777777777777777777777777777777777999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888888877777777777777777777777777777777777777777799999999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888877777777777777777777777777777 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
0.67777777777777777777777777777777777777777777777777777777777777777777777777777777777777777799999999999999999999999999999999999999999999999999999999999999888888888888888888888888888888888888888888888888888888888888888888888888877777777777777777777777777777777777777777777777777777799999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888888888777777777777777777777777777777777777777777777777999999999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888877777777777777777777777777777777777777777777999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888888877777777777777777777777777777777777777777799999999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888877777777777777777777777777777 = 0.67777777777777777777777777777777777777777777777777777777777777777777777777777777777777777799999999999999999999999999999999999999999999999999999999999999888888888888888888888888888888888888888888888888888888888888888888888888877777777777777777777777777777777777777777777777777777799999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888888888777777777777777777777777777777777777777777777777999999999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888877777777777777777777777777777777777777777777999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888888877777777777777777777777777777777777777777799999999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888877777777777777777777777777777/1 = 6.7777777777778/10 = 67.777777777778/100 = 677.77777777778/1000 = 6777.7777777778/10000 = 67777.777777778/100000 = 677777.77777778/1000000 = 6777777.7777778/10000000 = 67777777.777778/100000000 = 677777777.77778/1000000000 = 6777777777.7778/10000000000 = 67777777777.778/100000000000 = 677777777777.78/1000000000000 = 6777777777777.8/10000000000000 = 67777777777778/100000000000000
And finally we have:
0.67777777777777777777777777777777777777777777777777777777777777777777777777777777777777777799999999999999999999999999999999999999999999999999999999999999888888888888888888888888888888888888888888888888888888888888888888888888877777777777777777777777777777777777777777777777777777799999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888888888777777777777777777777777777777777777777777777777999999999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888877777777777777777777777777777777777777777777999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888888877777777777777777777777777777777777777777799999999999999999999999999999999999999999999999999988888888888888888888888888888888888888888888877777777777777777777777777777 as a fraction equals 67777777777778/100000000000000
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