0
Yes. Any number with a decimal representation that terminates or repeats must be a rational number. If it terminates, it's obviously rational. For example, 0.12345 is clearly 12345/100000, and the same is true for any other decimal; simply multiply it by a power of ten large enough to convert it to an integer, and then for the fraction put that integer over that power of ten.
Repeating is a little trickier; it may be best to illustrate with a couple of examples. Take the decimal 0.3333.... This multiplied by ten is 3.333...., and subtracting the original number obviously gives 3 exactly, so 10x - 1x = 9x = 3; x = 3/9 which reduces to 1/3. If it repeats in an alternating sequence (0.545454...) it's necessary to use a larger power of ten: 100x - 1x = 99x = 54; x = 54/99 = 6/11.
One or the other of these can be done for any terminating or repeating decimal expansion, therefore they must be rational.
Still curious? Ask our experts.
Chat with our AI personalities
Ezra
Maxine
ReneAdd your answer:
Earn +20 pts
Is 3.40764076407640764076 rational or irrational?
3.407640764076407640764076(not repeating) is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. ---- 3.407640764076407640764076 = 3407640764076407640764076/1000000000000000000000000 Which is of the form of one_integer/another_integer so it a rational number. 3.4076... (where the 4076 repeats forever): 3.4076... = 34076/9999 = 34073/9999 Again of the form of one_integer/another_integer so it a rational number. Either way, 3.4076...4076 is a rational number. Decimal numbers that terminate, or go on forever with repeating a sequence of digits are rational. Decimal numbers that go on forever without repeating a sequence of digits are irrational, eg √2.
Is -9pie rational or irrational?
What is 'pie' ; the meat pie that you eat??? I think you mean 'pi' , the mathematical symbol. Please spell it correctly.!!!!! pi = 3.141592654.... is an irrational number. Casually, an IRRATIONAL number is one which the decimals go to infinity and the decimal digits are not in any regular order. Any number rattional or irrational multiplied to aN IRRATIONAL number produces an irrational result. Hen ce -9 is rational -9(3.141592654...) = -28.27433388... is irrational.
Which number produces an irrational number when multiplied by?
At least one of the factors has to be irrational.* An irrational number times ANY number (except zero) is irrational. * The product of two irrational numbers can be either rational or irrational.
Is 4.121314 is a rational number or irrational?
it is a rational number but 4.121314..... is an irrational no
What number do you get when you add an irrational and a rational number?
An irrational number.
