Question

Show that 0.4777.......can be expressed in the form of p/q, where p and q are integers and q≠0

Answer 1

Let,
x = 0.47777.......
10x = 4.7777... - i
100x = 47.7777... - ii

Now, from i and ii we get,

100x - 10x = 47.777 - 4.777
90x = 43
x = 43/90
x = 0.4777777778.

Hope that helps you ☺☺

#Be brainly ✌✌

Answer 2

yes it can be expressed.
let's do it...
$x = 0.4777...$
hence,
$x = 0.47 bar(only \: on \: 7)$
$10x = 0.47bar \times 10$
now you'll be wondering why we have multiplied both sides by 10 only....we multiply both sides by seeing how many digits are under bar here there is only 1 hence we take 10 with only 1 zero after 1 ...as the no. of digits are increased under the bar The number of zeros will increase after one which will be multiplied on both the sides.
$10x = 4.7bar$
$10x = 4.3 + 0.47bar$
$10x = 4.3 + x$

$9x = 4.3$
$x = 4.3 \div 9$
$x = 43 \div 90$