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0.194805194805...

Convert the decimal into a fraction.

User Yotka
by
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1 Answer

3 votes

Answer:

  • The fraction is 15/77

Explanation:

The repeated part is 194805, six digits. Let the fraction be x.

Convert as follows:

  • 1000000x - x = 194805.194805 ... - 0.194805 ...
  • 999999x = 194805
  • x = 194805/999999

Find prime factors of both numerator and denominator and simplify by cancelling common factors:

  • 194805 = 3⁴*5*13*37,
  • 999999 = 3³*7*11*13*37.

The common factors are:

  • 3³*13*37

When they cancel we are left with:

  • x = (3*5)/(7*11)
  • x = 15/77

User Mohamed Gallah
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