Question

Write the p/q form for 1.272727....

Answer 1

Answer:

1

Step-by-step explanation:

multiply by 100

100x =127. 272727..........1

multiply by 10

x =1.727272........2

subtract 1 from 2

99x = 126

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Answer 2

Answer:

126/99

(For proof , refer to the attachment ^_^")

Note:

★ Rational number : The number which can be written in the form of p/q where p and q are integers and q ≠ 0 , is called rational number .

★ Rational numbers are characterized as ;

1). Terminating

2). Non-terminating but repeating

( Non-terminating but recurring )

★ Every terminating decimal and Non-terminating but repeating decimal can be represented in the form of p/q .

Solution:

Let the given number be x .

Thus,

x = 1.272727... -------(1)

Now,

Multiplying both sides of eq-(1) by 100 ,

We have ;

=> 100x = 100 × 1.272727...

=> 100x = 127.272727... --------(2)

Now,

Subtracting eq-(1) from eq-(2) , we get ;

=> 100x - 10x = 127.272727... – 1.272727...

=> 99x = 126

=> x = 126/99

=> 1.272727... = 126/99

Hence,

Required answer is 126/99 .