Question

0.194805194805...

Convert the decimal into a fraction.

Answer 1

• 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