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What is 2.0145 repeating as a fraction?

 Oct 28, 2014

Best Answer 

 #1
avatar+23254 
+5

Does 0145 repeat or does just 145 repeat?

If the number is 2.014501450145...

Let n = 2.01450145...

Then multiply by 10000, to move a 4-digit array:

                10000n = 20145.01450145...

                         n =         2.01450145...

Subtract:    9999n  =  20143.00000...

                         n  =  20143 / 9999

If the number is 2.0145145145...

Let n = 2.0145145145...

Then multiply by 1000, to move a 3-digit array:

                 1000n = 2014.5145145...

                         n =      2.01450145...

Subtract:      999n  =  2012.500000...

                         n  =  2012.5/999  =  20125/9990  =  4025/1998

 Oct 28, 2014
 #1
avatar+23254 
+5
Best Answer

Does 0145 repeat or does just 145 repeat?

If the number is 2.014501450145...

Let n = 2.01450145...

Then multiply by 10000, to move a 4-digit array:

                10000n = 20145.01450145...

                         n =         2.01450145...

Subtract:    9999n  =  20143.00000...

                         n  =  20143 / 9999

If the number is 2.0145145145...

Let n = 2.0145145145...

Then multiply by 1000, to move a 3-digit array:

                 1000n = 2014.5145145...

                         n =      2.01450145...

Subtract:      999n  =  2012.500000...

                         n  =  2012.5/999  =  20125/9990  =  4025/1998

geno3141 Oct 28, 2014

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