Express the recurring decimal 0.3 as an infinite GP and find its value in rational form
Answers
Answered by
5
Step-by-step explanation:
Let x=0.
3
ˉ
=0.3333...
=0.3+0.03+0.003+0.0003+...
=
10
3
+
100
3
+
1000
3
+...
=
1−
10
1
10
3
=
9
3
=
3
1
.
Let y=1.2
3
ˉ
=1.233333
=1.2+0.03+0.003+0.0003+...
=1.2+
10
2
3
+
10
3
3
+
10
4
3
+...
=1.2+
1−
10
1
10
2
3
=1.2+
30
1
=
30
37
.
Answered by
3
Answer:
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