Question

# Express 0.254545454...... as a fraction in the simplest form

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Solution

## First, we are going to give our decimal a name, let's call it x. We notice that x repeats after two digits, so how about we look at 100x. 100x = 25.4545454... But, the decimal part of this number is what we called x, so let's subtract it. 1000x - 10x = 254.5454545... - 2.54545454 Working out both sides, we get 990x = 252 So, x = 252/990. However, we are not finished as the question said "in its simplest form". Either notice that 990 and 252 are both divisible by 9, or that they're divisible by 3 twice and we get the final answer. x = 28/110 Which is divisible by 2 X= 14/55

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