# i) Explain using algebra, that the fractions gets closer and closer to ii) Using the general principle above on single digit numbers, find the decimal forms of (why are left out in this?)iii) What can we say in general about those decimal forms in which a single digit repeats?

i) We can easily see that

Since,

Thus, get closer and closer to

ii) From part (i),

We can write

are excluded because they in these fractions numerator and denominator have common factors.

iii) The decimal forms in which a single digit repeat are generally those in which we get the same remainder after each step. These forms are called repeating or recurring decimal forms.

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