1/3 does not terminate.
As a decimal, 0.076923 repeating
If the remainder were 0 it would be a terminating decimal. So it it not one of them. Any rational fraction MUST be have a decimal representation that is either terminating or recurring. So it is a recurring decimal.If you carry on with the division, you may find that the remainder changes but it will return to an earlier value. The part of the "quotient" from where you first got the remainder to where you got it again is the string of repeating digits. It will always be less than the denominator of the fraction.So, for example,2/3 = 0.66.... has a repeating string of length 1 but2/7 = 0.285714 285714 .... has a repeating string of length 6 = 7-1.2/13 = 0.153846 153846 ... also has a repeating string of length 6.
13/22 cannot be expressed as a terminating decimal because the divisor has a factor other that 2 or 5.
1/3, 1/6, 1/7, 1/9, 1/11, 1/12, 1/13, 1/14, 1/15 all have repeating decimal representations, while 1/2, 1/4, 1/5, 1/8, 1/10, and 1/16 have terminating decimal representations.
1/3 does not terminate.
As a decimal, 0.076923 repeating
That depends how the decimal is defined. If you have a fraction, and convert it to a decimal:* If the fraction, in simplest terms, only has the prime factors 2 and 5 in its denominator, the corresponding decimal number is terminating. This is related to the fact that 2 and 5 are the factors of 10 (the base of our decimal system). For example, a denominator of 2, 4, 5, 8, 10, 16, 32, 125, 625, 20, etc., will be terminating.* If there is any other prime factor in the denominator, the corresponding decimal number will repeat periodically. This is the case with denominators such as 3, 6, 7, 9, 11, 12, 13, etc.
If the remainder were 0 it would be a terminating decimal. So it it not one of them. Any rational fraction MUST be have a decimal representation that is either terminating or recurring. So it is a recurring decimal.If you carry on with the division, you may find that the remainder changes but it will return to an earlier value. The part of the "quotient" from where you first got the remainder to where you got it again is the string of repeating digits. It will always be less than the denominator of the fraction.So, for example,2/3 = 0.66.... has a repeating string of length 1 but2/7 = 0.285714 285714 .... has a repeating string of length 6 = 7-1.2/13 = 0.153846 153846 ... also has a repeating string of length 6.
If the remainder were 0 it would be a terminating decimal. So it it not one of them. Any rational fraction MUST be have a decimal representation that is either terminating or recurring. So it is a recurring decimal.If you carry on with the division, you may find that the remainder changes but it will return to an earlier value. The part of the "quotient" from where you first got the remainder to where you got it again is the string of repeating digits. It will always be less than the denominator of the fraction.So, for example,2/3 = 0.66.... has a repeating string of length 1 but2/7 = 0.285714 285714 .... has a repeating string of length 6 = 7-1.2/13 = 0.153846 153846 ... also has a repeating string of length 6.
If the remainder were 0 it would be a terminating decimal. So it it not one of them. Any rational fraction MUST be have a decimal representation that is either terminating or recurring. So it is a recurring decimal.If you carry on with the division, you may find that the remainder changes but it will return to an earlier value. The part of the "quotient" from where you first got the remainder to where you got it again is the string of repeating digits. It will always be less than the denominator of the fraction.So, for example,2/3 = 0.66.... has a repeating string of length 1 but2/7 = 0.285714 285714 .... has a repeating string of length 6 = 7-1.2/13 = 0.153846 153846 ... also has a repeating string of length 6.
If you mean repeating 8 then it is: 5/36
13/22 cannot be expressed as a terminating decimal because the divisor has a factor other that 2 or 5.
-612
0.173333 repeating
1/3, 1/6, 1/7, 1/9, 1/11, 1/12, 1/13, 1/14, 1/15 all have repeating decimal representations, while 1/2, 1/4, 1/5, 1/8, 1/10, and 1/16 have terminating decimal representations.
13 is not a fraction and so its decimal equivalent is 13.