Vikram claims that 0.4545... (the repeating decimal 0.45 bar) lies between 4/9 and 5/9. Using 4/9 = 0.444... and 5/9 = 0.555..., is his claim true?

Question

Accepted Answer

True; 0.4545... is between 0.444... and 0.555.... 4/9 = 0.444..., 5/9 = 0.555..., and 0.4545... lies between these, so the claim is true.

Vikram claims that 0.4545... (the repeating decimal 0.45 bar) lies between $\frac{4}{9}$ and $\frac{5}{9}$ .
Using $\frac{4}{9} = 0.444...$ and $\frac{5}{9} = 0.555...$ , is his claim true?