One of the most common methods used to convert a repeating, nonterminating decimal to a fraction is by using the long division method. This involves writing out the decimal as an infinitely long string of digits and then dividing it into two parts – one part is ‘longer’ than the other but both parts contain exactly the same sequence of numbers with no gaps or omissions. Then, you can find what fraction these two parts represent by taking the second part (the shorter one) and expressing it as a fraction over one with the same number of digits in each part. For example: 0.72 = 7/10 + 2/100 = 70/100.
Another method that can be used to convert a repeating, nonterminating decimal to a fraction is called “repeating decimals”. This involves breaking down each repeating block into its own separate unit and expressing them in fractions over powers of 10. For instance, 0.141414…can be expressed as 1/7 + 4/70 + 4/700 + etc., which can then be further simplified by finding common denominators for all terms so that they are expressed in their lowest form.
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