Question

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

Answer 1

Step-by-step 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:

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

We have

$\dfrac{2}{11}\\\\11-\text{prime number}\\\\\text{the decimal is infinite r}\text{epeating}$