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Polynomials

Question
CBSEENMA9001487

Express 0. top enclose 001 in the form of straight p over straight q where p and q are integers and q ≠ 0.

 

Solution

Let straight x equals 0. top enclose 001

Then, x = 0.001 001 001 001...... ...(1)
⇒ 1000x = 1.001 001 001 001...... ...(2)
Subtracting (1) from (2), we get
99x = 1
rightwards double arrow space space space space space space space space straight x equals 1 over 99
rightwards double arrow space space space space space space space space straight p equals 1 comma space space space straight q space equals space 999 space left parenthesis not equal to 0 right parenthesis

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Find two rational numbers between 0.1 and 0.2.