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Elena and Han are discussing how to write the repeating decimal x=0.137 as a fraction. Han says that 0.137 equals 1376499900. “I calculated 1000x=137.777 because the decimal begins repeating after 3 digits. Then I subtracted to get 999x=137.64. Then I multiplied by 100 to get rid of the decimal: 99900x=13764. And finally I divided to get x=1376499900.” Elena says that 0.137 equals 124900. “I calculated 10x=1.377 because one digit repeats. Then I subtracted to get 9x=1.24. Then I did what Han did to get 900x=124 and x=124900.”
Do you agree with either of them? Explain your reasoning.
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