Question

express 0.2353535... = 0.235 in the form of p/q​

Answer 1

Answer:

Answer:

Given a number 0.2353535…….

We need to prove 0.2353535… = 0.235‾ can be expressed in the form of p/q, where p and q are integers and q ≠zero

Proof:

Let us assume that

x = 0.2353535…

x = 0.235 ——————(i)

On Multiplying both sides by 100 of equation (i) we get,

100x = 100 × 0.2353535…

100x = 23.53535————–(ii)

Subtracting equation (i) from equation (ii) we get,

100x – x = 23.53535 – 0.2353535…

99x = 23.2999965

x = 23.2999965/99

x = 233/990

x = 0.2353535

Hence, x = 0.2353535…= 0.235‾ can be expressed in the form of p/q as 233/ 990 and here q=990 (q≠zero)

Hence proved.

Answer 2

Answer:

x=0.235

multiply by 10

10x=2.35______(1)

multiply again by 100

10×100x=235.35

1000x=235.35______(2)

subtract (1) from (2)

1000x-10x=235.35-2.35

990x=233

x=233/990

explanation:

in this question only 35 term is repeated term