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Question
Write the following in decimal form and say what kind of decimal expansion has:
`3/13`
Solution
Dividing 3 by 13, we get
`13)overline(3.00000000)(0.23076923...`
-26
40
-39
10
-00
100
-91
90
-78
120
-117
30
-26
40
-39
1
Here, the repeating block of digits is 230769.
∴ `3/13` = 0.23076923...
= `0.overline230769`
Thus, the decimal expansion of `3/13` is non-terminating repeating.
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