Why is it helpful to convert fractions to decimals and decimals to fractions?

Essense of decimal is still fraction: 3.14=3+1/10+4/100. It is a way to represent a fraction by a set of common denominators: 1/10, 1/100...

The advantage of decimals is that because all of them are in common denominators already, addition, subtraction and comparing are quite straightforward.

To convert decimal to fraction is very simple, 3.14=314/100. However, the advantage of fraction is the freedom to
**not** use the common denominators: 314/100=157/50. In some cases, fraction can be more accurate and much simpler, for instance, 1/3=0.33333.....(forever). On a calculator, it can only display and handle so many digits of decimal and would never really compute a simple fraction like 1/3. Try it on your own calulator: 1/3=0.3333333, X3=0.9999999, it doesn't not go back to 1 and there the accuracy is lost.

That said, in real life, we mostly deal with limited number of decimal digits, whether in measuring how tall a kid is or figuring out how many dallors needed for a bill. Decimal is a great tool for day to day stuff.

Hope it helps.