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larisa [96]
3 years ago
13

Express 1.21212121.... as a fraction

Mathematics
2 answers:
Elodia [21]3 years ago
7 0
That would be 1 21/99  or  120/99 as an improper fraction.
aksik [14]3 years ago
5 0

To solve such questions we will have to observe the fact that this is a repeating decimal number with the repeating figures being 2 and 1 as 21.

Thus, we can represent 1.21212121... as 1.\overline{21}

Let us represent the original number 1.21212121... by the letter "a". Thus,

a=1.21212121...=1.\overline{21}

Therefore,a=1.\overline{21}..................(equation 1)

Let us now multiply (equation 1) by 100 to get:

100a=100\times 1.212121...=121.\overline{21}.....(equation 2)

Now, when we subtract (equation 2) from (equation 1), we will get:

100a-a=121.\overline{21}-1.\overline{21}

99a=120

\therefore a=\frac{120}{99}

Thus the given number 1.21212121... can be represented as a fraction as \frac{120}{9}.



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