1.Why can you use either a fraction or a decimal to name the same rational number?

Answer 1

in general, you can't, unless the denominator has factors of only 2 and 5, which are divisors of 10.

2/3 = 0.66666...
so it cannot be represented exactly as a decimal.

But any terminating or repeating decimal represents a rational number, since it can be multiplied by a power of 10 to produce an integer.

0.3627 = 3627/10000
0.263263263263... = 263/999