Answer :

Final answer:

To convert 1.37 with repeating 37 to a fraction, declare it as x and multiply it by 100 to push the repeating part after the decimal point. Subtract the two resulting equations, resulting in x = 136/99. After simplifying by dividing both numbers by 2, the simplest form is 68/49.5.

Explanation:

To express 1.37 bar, where the bar stands for a repeating decimal pattern in the number, as a rational number in the simplest form, we first let the repeating part of the decimal be x. So, x = 1.37 bar where 'bar' means the digits 37 repeat indefinitely. A clever trick to remove the bar or repeated digits is to multiply x by a power of 10 that pushes the repeating part after the decimal point. Here, as there are two digits repeated, we can write 100x = 137.37 bar. If we subtract the two equations, we get 99x = 136. Therefore, x = 136/99. To simplify, we can note that both the numerator and the denominator are divisible by 2. Hence, the simplest form of 1.37 bar as a rational number is 68/49.5.

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