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That's because all repeating decimals can be converted into fractions. Here is an example: 4.161616... Let's call this number "x". Multiply by 100 (use a "1" followed by two zeroes in this case, because the repetition period is two), and write:
100x = 416.161616...
x = 4.161616...
Subtract the two equations:
99x = 412
x = 412 / 99
So there you have it - the number was converted to a fraction made up of integers - which is exactly the definition of "rational number".
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All repeating decimals are rational numbers?
Yes.
Are all terminating and repeating decimals rational numbers Explain?
Yes, they are.
What is the set of all integers plus all of the termination or repeating decimals?
The rational numbers
Are all nonterminating decimals irrational numbers?
Not at all. 0.33333... nonterminating = 1/3 rational 0.66666... nonterminating = 2/3 rational 0.1428571428... nonterminating = 1/7 rational 0.55555... nonterminating = 5/9 rational
Are all terminating and decimals rational numbers?
All terminating decimal numbers are rational.
Is a rational number a repeating decimal?
All repeating decimals are rational numbers. Not all rational numbers are repeating decimals.
All repeating decimals are rational numbers?
Yes.
Are all terminating and repeating decimals rational numbers Explain?
Yes, they are.
Are all terminating and repeating numbers rational numbers?
All decimals that terminate, or end with a repeating set of digits are rational numbers. eg 1.234, 1.222..., 1.232323..., 1.23444..., 1.2343434... are all rational numbers.
What is the set of all integers plus all of the termination or repeating decimals?
The rational numbers
Why can't repeating decimals be a rational number?
If the decimal representation of a number repeats, it isa rational number.
Are all nonterminating decimals irrational numbers?
Not at all. 0.33333... nonterminating = 1/3 rational 0.66666... nonterminating = 2/3 rational 0.1428571428... nonterminating = 1/7 rational 0.55555... nonterminating = 5/9 rational
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.
Is 39.81 repeating rational?
Yes it is. Repeating decimals are all repeating rationals.
Is 1 9 a rational number?
yes, all numbers except numbers that have non-terminating, non-repeating decimals.
What includes the integers and all terminating and repeating decimals in the real system?
The set of rational numbers (ℚ).
Are all terminal and repeating decimals rational?
Yes.
