Question

Express each of the following decimals in the p/q form
(1) 0.46bar
() 0.792bar​

Answer 1

1.let x=0.46bar

then x=0.464646...... -(1)

multiplying equation 1 from 100 we get,

100x=46.464646......-(2)

now, subtracting equation 1 from 2 we get,

100x-x=46.464646....-0.464646.....

99x=46

x=46/99

2.let x=0.792 bar

then x = 0.796796.....-(1)

multiplying equation 1 with 1000 we get

1000x=796.796796.....-(2)

now subtracting equation 1 from 2 we get

1000x-x=796.796....-0.796.....

999x=796

x=796/999