Question

ao efetuar a divisão entre dois numeros inteiros positivos, obteve como resultado a dizima periodica 0,57. para obter um numero natural maior que essa dizima, tem que adicionala a que fração

Answer 1

I will answer in English:

We first have a rational number, the quotient between 2 positive integer numbers is 0.57....

And we want to find which number we should add in order to get 1.

Then we have:

A/B = 0.5757...

So if we have:

x = 0.5757....

we have two periodic decimals, then we multiply by 100 (the number of zeros is equal to the number of periodic decimals)

100*x = 57.575757

Now we subtract the original number:

100*x - x = 99*x = 57.575757... - 0.5757 = 57.

Then we have:

99*0.5757... = 57

0.575757... = 57/99

Now that we know the original fraction, if we want to find a fraction such that:

0.57... + a/b = 1

57/99 + a/b = 1

we should use the same denominator in both fractions:

b = 99

57/99 + a/99 = 1

57 + a = 99

a = 99 - 57 = 42

Then the fraction is 42/99