Show that 0.2353535... = 0.235 can be expressed in the form p/q, where p and q are integers and q ≠ 0.
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Answered by
46
Answer:
Answer: 0.2353535... = 0.235 can be expressed as 233/99 i.e., in the form of p/q, where p and q are integers and q is not equal to zero.
Answered by
15
A rational number can have two types of decimal representations (expansions):
- Terminating
- Non-terminating but repeating
0.2353535... is a non-terminating but repeating decimal, it is denoted by 0.2¯350.235¯.
let x = 0.2353535...
100x = 235.353535...
100x - x = (235.353535...) - (2.353535...)
99x = 233
x = 233/99
Therefore, 0.2353535... = 0.235... = 233/99 can be expressed in the rational form.
Thus, 0.2353535...= 0.235 can be expressed as 233/99 i.e., in the form of p/q, where p and q are integers and q is not equal to zero
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