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".
Yes.
Yes, they are.
The rational 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
Rational numbers can be classified into two main types: terminating decimals and repeating decimals. Terminating decimals are numbers that have a finite number of digits after the decimal point, while repeating decimals have one or more digits that repeat infinitely. Both types can be expressed as fractions, where the numerator is an integer and the denominator is a non-zero integer. Overall, rational numbers encompass all numbers that can be represented in this fractional form.
All repeating decimals are rational numbers. Not all rational numbers are repeating decimals.
Yes.
Yes, they are.
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.
The rational numbers
If the decimal representation of a number repeats, it isa rational number.
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
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.
Yes it is. Repeating decimals are all repeating rationals.
yes, all numbers except numbers that have non-terminating, non-repeating decimals.
The set of rational numbers (ℚ).
Yes.