23.6 repeating in fraction notation
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To write 23.6 repeating in fraction notation, we can use the concept of infinite repeating decimals and convert it to a fraction.
Step 1: Let's denote the repeating decimal as "x": x = 23.6 (repeating)
Step 2: Multiply both sides of the equation by 10 to remove the repeating decimal: 10x = 236.6 (repeating)
Step 3: Subtract the original equation from the equation obtained in the previous step: 10x - x = 236.6 - 23.6
Simplifying the equation, we get: 9x = 213
Step 4: Divide both sides of the equation by 9: x = 213/9
Thus, the fraction notation for the repeating decimal 23.6 is 213/9. However, we can simplify the fraction further:
Step 5: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which in this case is 3: 213/9 = 71/3
So, 23.6 (repeating) in fraction notation is 71/3.