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In a non-zero fraction is written in its simplest form, then if the denominator has any prime factor other than 2 or 5 it will not go into any numerator evenly. This leads to repeating decimals.

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Q: Why do some decimals repeat and some decimals not repeat?
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What does terminating decimal mean?

Some decimals repeat. Some decimals go on forever. Some decimals stop. Those are called terminating decimals.


What is the meaning of recurring decimal?

Some decimals stop, some keep on going. The ones that repeat are known as recurring decimals.


Why do decimals repeat?

Decimals repeat because there is no definite end. In these, you can end the repeat by rounding up... (Exp: 4.44444444444444... would be 4.45 or 4.445 or 4.4445, etc.


What does non terminating non repeating mean?

Some decimals terminate. (0.3) Some decimals repeat (0.3333333) Some do neither. Pi is the most famous example. 3.1415 etc.


What is non repeating decimals?

That can refer to one of two types of decimals: terminatingand irrational.Terminating decimals don't repeat because they stop, whereas irrational decimals simply never repeat a distinct pattern of digits.


Do all irrational decimals repeat?

No, none of them do.


What are the 3 kinds of decimals?

The 3 kinds of decimals are "terminating" "recurring" and "other" Terminating decimals are ones that end, such as 0.74 or 0.19857 Recurring decimals are ones that don't end, but repeat, such as 0.6666666... or 0.142857142857142857.... Other decimals don't end, and don't repeat, but go on forever, such as pi=3.14159265358979323.....


What are special kinds of decimals?

There are irrational numbers (like PI and e) that have infinitely many decimals which do not repeat and rational numbers (the quotient of two integers) which do eventually repeat.


Why are there repeating decimals?

Some numbers cannot be written exactly and their decimals repeat infinitely. The best example is 1/3 written as a decimal. It is 0.33333 going on infinitely. Some have multiple digits that keep repeating.


What is the difference between the decimal expansion in irrational and rational numbers?

Decimals that terminate or repeat in some fashion are rational, while decimals that expand forever are irrational.


What is 309 divided by 7?

44.1429


Are repeating decimals rational?

Yes. Rational numbers are numbers or decimals that repeat or terminate. Irrational numbers do not. For example π is an irrational number.