Show that 0.2353535...= 0.235 can be expressed in the form of p/q, where p and q are integers and q is not equal to zero
Answers
Given a number 0.2353535…….
We need to prove0.2353535…= 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…=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,
99x=23.53535…−0.2353535…
x= 23.33 / 99
x= 233/ 990
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
Given a number 0.2353535…….
We need to prove0.2353535…= 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…=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,
99x=23.53535…−0.2353535…
x= 23.33 / 99
x= 233/ 990
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