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Question:

Express the following in the formpq, where p and q are integers and q≠0. (i) 0.6 (ii) 0.47 (iii) 0.001001

Solution:

(i) Letx=0.666.. (1)Multiply by10we get10x=6.666 (2)Substract (1) from (2), we get9x=6⇒x=69=23Herep=2orq=3 (ii) Letx=0.47777.. (1)Multiply by10we get10x=4.7777 (2)Substract (1) from(2), we get9x=4.3⇒x=4.39=4390Herep=43orq=90 (iii) Letx=0.001001001.. (1)Multiply by1000we get1000x=1.001001 (2)Substract (1) from (2), we get999x=1⇒x=1999Herep=1orq=999.