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RossYou will get a repeating decimal if the denominator of a fraction has any factor other than 2 or 5.
Suppose there is a factor f. Then f can only leave a remainder of 1, 2, 3, ..., f-1. Whatever order you get these remainders, after at most f-1 digits, you will get a remainder that you had before. This is where the decimal sequence goes into its repeating sequence.
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Are repeating decimals rational or irrational numbers?
Repeating decimals are rational numbers if there is a pattern, like 0.22222222. If it is not a pattern, like 0.568964329, it is an irrational number.
Are repeating decimals an irrational number?
A repeating decimal is a rational number. Its value is(the repeating set of digits)/(as many 9s as there are digits above).
What is the counterexample for the repeating decimals are closed under division?
Division by 0, which can also be written as 0.000... (repeating) is not defined.
What are the 3 types of rational numbers?
If you convert them into decimal form you can say there are terminating decimals, there are the integers, and there are repeating decimals. EX: 2.4 is a terminating decimal. 2.44444444... is a repeating decimal. 2 is an integer. all are rational numbers.
Are all imperfect square roots repeating decimals?
Yes. Because they have to be a rational number
Why are negative repeating decimals, rational?
If you convert repeating decimals into a fraction, you see that the repeating decimals are rational.
What causes the difference in terminating decimals and repeating decimals?
If a fraction is a rational number then if the denominator goes into the numerator or into the numerator multiplied by a power of 10, then you will have a terminating decimal. Otherwise it will be a repeating decimal.
What are 5 examples of non terminating repeating decimals?
terminating decimals repeating decimals
What are the different kinds of decimal?
terminating decimals non terminating decimals repeating decimals non repeating decimals
What is the definition for the word non-repeating decimals?
Non-repeating decimals is not a word but a phrase. Non-repeating decimals are irrational numbers.
What are signs for decimals?
terminating decimals and repeating decimals
How do you say repeating decimals in German?
Repeating decimals is periodische Dezimalzahlen in German.
Why these decimal representations are called repeating decimals?
Not all decimal representations are repeating decimals.
Did Albert Einstein invent repeating decimals?
No, Albert Einstein did not invent repeating decimals.
Are terminating and repeating decimals irrational numbers?
Terminating and repeating decimals are rational numbers.
Are non-repeating decimals irrational numbers?
No because non-repeating decimals may be terminating.But suppose you consider terminating decimals as consisting of repeating 0s. That is, 1/8 = 0.125 = 0.12500....Then all non-repeating decimals are irrational.
Is decimals ratios?
Terminating and repeating decimals are.
