How to convert 5.4178 bar in the form of p/q
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5.4178 bar is the rational number with the last four digits repeating infinitely.
5.4178 4178 4178 4178 ....
Simple rule to write in the rational number form is : 4178 is four digits. so take 0.0001. here 1 is in the 4 th decimal place. subtract it from 1 and get q. the numerator p = 0.4178, the given repeating number without bar on top.
p / q = 5.0 + [ 0.4178 / (1 - 0.0001) ] = 5.4173 / 0.9999
= 54173 / 9999
This can be obtained by using geometric progression formula too.
5.0 + 0.4178 + 0.00004178 + 0.0000 0000 4178 + ...
= 5.0 + 0.4178 [ 1 + 0.0001 + 0.0000 0001 + .. ]
= 5.0 + 0.4178 * 1 / [ 1 - 0.0001 ]
= 5.0 + 0.4178 / 0.9999 = 5.4173 / 0.9999 = 54173 / 9999
5.4178 4178 4178 4178 ....
Simple rule to write in the rational number form is : 4178 is four digits. so take 0.0001. here 1 is in the 4 th decimal place. subtract it from 1 and get q. the numerator p = 0.4178, the given repeating number without bar on top.
p / q = 5.0 + [ 0.4178 / (1 - 0.0001) ] = 5.4173 / 0.9999
= 54173 / 9999
This can be obtained by using geometric progression formula too.
5.0 + 0.4178 + 0.00004178 + 0.0000 0000 4178 + ...
= 5.0 + 0.4178 [ 1 + 0.0001 + 0.0000 0001 + .. ]
= 5.0 + 0.4178 * 1 / [ 1 - 0.0001 ]
= 5.0 + 0.4178 / 0.9999 = 5.4173 / 0.9999 = 54173 / 9999
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