## anonymous one year ago Identify the number that does not belong with the other three. Explain your reasoning. 50.1 repeating 1, negative 50 over 2, negative 50.1, square root 50

Let's quickly go over rational and irrational numbers A rational number is a number which can be expressed in the form of $\frac{p}{q}$ where $q \neq 0$ and $p,q \in \mathbb{Z}$ that is p and q are integers irrational numbers r just opposite Let's look at first number, $50.111...$ Let $S=50.111....$ therefore $10S=501.111...$ Multiplying by 10 will take 1 out from the decimal, but still an infinitely amount of 1's in subtracting 2nd equation by first we get $10S-S=(501.111...-50.111...)=(501-50)+(0.111...-0.111...)$ We have simply taken the decimal parts apart it's the same as writing $2.34=2+0.34$ Now we have $9S=451$$S=\frac{451}{9}$ Which is of the form $\frac{p}{q}, p,q \in \mathbb{Z}, q \neq 0$ If you do the division of 451 by 9 in a calculator you will indeed get your number back again Thus 50.111..... is a RATIONAL number, in general all numbers with terminating decimals(decimals that end after some numbers) eg. $2.45$$55.2$ and numbers with non terminating and repeating decimals(decimals that keep on repeating to infinity) $2.474747...$ $5.77777...$ are RATIONAL But if a number has non terminating and NON repeating decimals, it is IRRATIONAL eg. infamous pi $\pi = 3.14159...$ You will never find a pattern that is repeating in the decimal expansion of pi Note that 22/7 is an approximation of pi, pi does not equal to 22/7 $\pi \approx \frac{22}{7}$ another eg. $\sqrt{2}=1.4142....$ In general square root of a number which is not a prefect square is IRRATIONAL By perfect square I mean a number who has a simple and integer square root $\sqrt{4}=2$ So 4 is a perfect square, it has an integer square root but root 2 cannot be written as an integer so it is an irrational number Your 2nd number $-\frac{50}{2}=-25$ It is a rational number where the denominator is 1(an integer not equal to 0) and numerator is also integer(-25) similarly your 3rd number has a terminating decimal, so it's a rational number however what about $\sqrt{50}$ rational or irrational?? The notation $p,q \in \mathbb{Z}, q \neq 0$ Means p and q are integers and q is not equal to zero