express each of the following decimals in the rational form p/q is 12.2bar8
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Let,
x=12.2 8bar
=12.28888...
Since one digit it repeating, we multiply 10 to get
10x=10*12.28888...
=> 10x=122.8888...
=> 10x=110.6+12.28888...
=> 10x=110.6+x
=> 10x-x= 110.6
=> 9x=110.6
=> x=110.6/9
=> x=1106/90
=> x=553/45
.·. The p/q form of 12.2 8bar is 553/45.
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