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recurring decimal

by sanju09 » Tue Mar 03, 2009 4:55 am
The value of the recurring decimal number 0.6313131... is equal to

A. 65/106
B. 125/198
C. 627/990
D. 691/1124
E. 737/1200
The mind is everything. What you think you become. -Lord Buddha



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by Baldini » Tue Mar 03, 2009 5:46 am
Answer is B.
So you by any chance know a shortcut for this type of exercise?
thx
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by bluementor » Tue Mar 03, 2009 5:55 am
0.631313131....
= 0.6 + 0.0303030303.. + 0.001010101...
= 0.6 + 3/99 + 0.001010101...
= 0.6 + 3/99 + (0.01010101...)/10
= 0.6 + 3/99 + (1/99)/10
=0.6 + 3/99 + (1/990)
=3/5 + 31/990
=(3(198) + 31)/990
= 625/990
=125/198

Choose B.

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by sanju09 » Tue Mar 03, 2009 6:05 am
Baldini wrote:Answer is B.
So you by any chance know a shortcut for this type of exercise?
thx
Sure Baldini, if the repeating pattern of digits is set to start right after the decimal point, then this part will be equivalent to the integer formed by pattern divided by as many 9s as are the digits in the numerator; for example 0.861861861... will always be equal to 861/999; 3.057575757... = 3 + 0.057575757... = 3 + (1/10) (0.57575757...) = 3 + (1/10) (57/99) = 3 + (1/10) (19/33) = 3 + (19/330) = 1009/330.

The present number

0.6313131... = 0.6 + 0.0313131... = 6/10 + (1/10) (0.313131...)

= 3/5 + (1/10) (31/99) = 3/5 + 31/990 = [(198*3) + 31]/990

= (594 + 31)/990 = 625/990 = 125/198
The mind is everything. What you think you become. -Lord Buddha



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by Baldini » Tue Mar 03, 2009 6:20 am
thanks a lot.
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