H5. Express 3.4 overline{17}=3.4171717 ldots using a geometric series, then write it as a ratio of two integers.

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Accepted Answer

Step:1 ：Let (x = 3.4overline{17})Step:2 ：Multiply both sides by 100 to get (100x = 341.overline{17})Step:3 ：Subtract the original equation from the new one to get (99x = 337.75)Step:4 ：Divide both sides by 99 to get (x = frac{337.75}{99})Step:5 ：Multiply both the numerator and the denominator by 4 to get rid of the decimal in the numerator, resulting in (x = frac{1351}{396})Step:6 ：Therefore, (3.4overline{17} = boxed{frac{1351}{396}})

Answer

Step: 1 ：Let (x = 3.4overline{17})Step: 2 ：Multiply both sides by 100 to get (100x = 341.overline{17})Step: 3 ：Subtract the original equation from the new one to get (99x = 337.75)Step: 4 ：Divide both sides by 99 to get (x = frac{337.75}{99})Step: 5 ：Multiply both the numerator and the denominator by 4 to get rid of the decimal in the numerator, resulting in (x = frac{1351}{396})Step: 6 ：Therefore, (3.4overline{17} = boxed{frac{1351}{396}})

H5. Express $3.4 \overline{17}=3.4171717 \ldots$ using a geometric series, then write it as a ratio of two integers.

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