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Let the fraction be x.

Then x = 0.1555...

As one digit repeats multiply both sides by 10 to give:

10x = 1.555...

Now subtract the value of x from both sides:

→ 10x - x = 1.555... - 0.1555...

→ 9x = 1.4

Multiply both sides by 10 to remove the decimal point from the right hand side, and find the value of x as a fraction:

→ 90x = 14

→ x = 14/90 = 7/45

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Q: What is 0.15 with just the 5 repeating as a fraction?
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