how to convert a decimal number with a bar in top into p/q form
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it depends on the number of digits on top of which the bar is there
for example take
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0.45
the bar is over two digits
__
first assume x = 0.45
now as it is over two digits,
__
find 10²*x i.e 100x which in this case will be 45.45
__ __
now 100x - x = 45.45 - 0.45 = 45
⇒99x = 45
x = 45/99 = 5/11
__
therefore 0.45 = 5/11
for example take
__
0.45
the bar is over two digits
__
first assume x = 0.45
now as it is over two digits,
__
find 10²*x i.e 100x which in this case will be 45.45
__ __
now 100x - x = 45.45 - 0.45 = 45
⇒99x = 45
x = 45/99 = 5/11
__
therefore 0.45 = 5/11
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