Question

How do you know that the decimal gor 2/11 repeats without ending​

Answer 1

Explanation:

When we factorise the denominator into prime factors and there are only numbers 2 and 5, the decimal is finite.

Otherwise the decimal is infinite repeating.

Examples:

`(3)/(20)\\\\20=2\cdot2\cdot5\to\text{decimal is finite}\\\\(3)/(20)=3:20=0.15\\---------------------\\(7)/(40)\\\\40=2\cdot2\cdot2\cdot5\to\text{decimal is finite}\\\\(7)/(40)=7:40=0.175\\---------------------\\(5)/(12)\\\\12=2\cdot2\cdot3\to\text{decimal is infinite r}\text{epeating}\\\\(5)/(12)=5:12=0.41666...=0.41\overline{6}`

We have

`(2)/(11)\\\\11-\text{prime number}\\\\\text{the decimal is infinite r}\text{epeating}`