Express the rational number 1/13 in recurring decimal form and hence write 69/13 in recurring decimal form.
Answers
Answer:
ep-by-step explanation:
Express : The rational number \frac{1}{33}
33
1
in recurring decimal form by using the recurring decimal expansion of \frac{1}{11}
11
1
.
Hence write \frac{71}{33}
33
71
in recurring decimal form.
Solution :
First we find the rational number \frac{1}{11}
11
1
in decimal form.
\frac{1}{11}=0.0909090909090..........
11
1
=0.0909090909090..........
Now, \frac{1}{33}
33
1
is re-written as
\frac{1}{33}=\frac{1}{3}\times\frac{1}{11}
33
1
=
3
1
×
11
1
\frac{1}{33}=\frac{1}{3}\times0.0909090909090........
33
1
=
3
1
×0.0909090909090........
\frac{1}{33}=0.0303030303030 ......
33
1
=0.0303030303030......
Now, To write \frac{71}{33}
33
71
in recurring decimal form
\frac{71}{33}=71\times\frac{1}{33}
33
71
=71×
33
1
\frac{71}{33}=71\times0.0303030303030 .......
33
71
=71×0.0303030303030.......
\frac{71}{33}=2.15151515151515 ..............
33
71
=2.15151515151515.............