IM 8.8.15 Practice: Infinite Decimal Expansions
Elena and Han are discussing how to write the repeating decimal as a fraction. Han says that equals . “I calculated because the decimal begins repeating after 3 digits. Then I subtracted to get . Then I multiplied by to get rid of the decimal: . And finally I divided to get." Elena says that equals . “I calculated because one digit repeats. Then I subtracted to get . Then I did what Han did to get and ." Do you agree with either of them? Explain your reasoning.
How are the numbers and the same? How are they different?
and . This gives some information about .
Without directly calculating the square root, plot on all three number lines using successive approximation.