On fraction of productsConsider 1 101 = 0.00990099 … and 1 143 = 0.00699300699300 … and 1 101 × 143 = 0.0000692376930000692376930000 …Now 990 × 69930 = 69230700 which is almost 69237693Is it possible to get exact equality? If so when should I truncate the fractions before multiplying?

Question

On fraction of productsConsider       1    101    =  0.00990099  … and       1    143    =  0.00699300699300  … and       1          101      ×      143        =  0.0000692376930000692376930000  …Now   990  ×  69930  =  69230700 which is almost   69237693Is it possible to get exact equality? If so when should I truncate the fractions before multiplying?

Alison Mcgrath · Accepted Answer

No. You ask whether it is possible to have      a                  10        n            −      1        ⋅      b                  10        m            −      1        =            a      b                      10        k            −      1        .Except for the trivial cases   a  =  0 or   b  =  0, this would require      10    k    −  1  =  (      10    n    −  1  )  (      10    m    −  1  )  =      10          n      +      m        −      10    n    −      10    m    +  1.As the left is   ≡  −  1    (  mod    10  ) and the right   ≡  +  1    (  mod    10  ), this cannot happen.

On fraction of products Consider 1/(101)=0.00990099…and 1/(143)=0.00699300699300… and 1/(101xx143)=0.0000692376930000692376930000…. Now 990xx69930=69230700 which is almost 69237693. Is it possible to get exact equality? If so when should I truncate the fractions before multiplying?

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