Either terminating (as in 0.25) or non-terminating as in the expression for pi.
To show a repeating decimal you put a dot above the digit that repeats.
As written it is a terminating decimal. However, if the digits 123456789101112 keep on repeating after the amount written (normally it would be written with a dot over the first 1 and the last 2; as that is impossible here, to show repeating an ellipsis (three dots) could be used, as in: 0.123456789101112123456789101112... to show that it goes on) then it is a repeating decimal.
when converting a fraction to a decimal, some of the answers will be repeating decimals. A bar or line is sometimes placed over the part of the decimal that keeps repeating. ex: 0.24242424 etc. can be written as 0.24 with a 'bar' over the 24 to show that it keeps repeating.
1/3 is .3333 repeating forever. To get this you divide 1 by 3.
Either terminating (as in 0.25) or non-terminating as in the expression for pi.
yes, repeating decimals (those that have infinite - never ending - number of digits after the decimal point and these decimals show repeating pattern) are rational numbers, because they can be written as fractions.
The decimal shows a repeating pattern. Repeating decimals are rational.
0.666 repeating
To show a repeating decimal you put a dot above the digit that repeats.
.2333 with the bar over the 333
As written it is a terminating decimal. However, if the digits 123456789101112 keep on repeating after the amount written (normally it would be written with a dot over the first 1 and the last 2; as that is impossible here, to show repeating an ellipsis (three dots) could be used, as in: 0.123456789101112123456789101112... to show that it goes on) then it is a repeating decimal.
when converting a fraction to a decimal, some of the answers will be repeating decimals. A bar or line is sometimes placed over the part of the decimal that keeps repeating. ex: 0.24242424 etc. can be written as 0.24 with a 'bar' over the 24 to show that it keeps repeating.
Sometimes. Ellipses are used in repeating decimals like 7.4444... or 8.121212... to show that the pattern repeats forever. Repeating decimals are rational. Ellipses are also used in non-repeating, non-terminating decimals like pi = 3.14159... . Non-repeating, non-terminating decimals are irrational.
In fact, the statement is true. Consequently, there is not a proper counterexample. The fallacy is in asserting that a terminating decimal is not a repeating decimal. First, there is the trivial argument that any terminating decimal can be written with a repeating string of trailing zeros. But, Cantor or Dedekind (I can't remember which) proved that any terminating decimal can also be expressed as a repeating decimal. For example, 2.35 can be written as 2.3499... Or 150,000 as 149,999.99... Thus, a terminating decimal becomes a recurring decimal. As a consequence, all real numbers can be expressed as infinite decimals. And that proves closure under addition.
1/3 is .3333 repeating forever. To get this you divide 1 by 3.
There cannot be a counterexample since the assertion is true. This requires you to accept the true fact that the terminating decimal 1.25, for example, is equivalent to the repeating decimal 1.25000... (or even 1.24999.... ).