why is 1.6666666667 an irrational number?
this was my answer to a question, and you also have to explain why your answer is an irrational number.
an irrational number is "any real number that can not be written and the quotient of two number"
but it can? so is it a rational number then?
WHAT DOES 16666666667 MEAN! YOU DIDN'T ELLS US WHAT IT MEANS!!!!! :p
1.6666666667 is NOT an irrational number.
(1.6666666667 = 16666666667/10000000000 , there! I wrote it as a rational number)
bot?
To determine whether 1.6666666667 is a rational or irrational number, we need to understand the definition of a rational number.
A rational number is any number that can be expressed as a fraction or a quotient of two integers. In other words, a number can only be considered rational if it can be written in the form a/b, where a and b are integers (whole numbers) and b is not zero.
In the case of 1.6666666667, it appears to be a decimal representation of a number. However, we can simplify it and write it as a fraction to see if it fits the definition of a rational number.
To convert 1.6666666667 into a simplified fraction, we can multiply it by 10 to eliminate the decimal places:
1.6666666667 * 10 = 16.666666667
Now, let's represent 16.666666667 as a fraction:
Let x = 16.666666667
To convert the decimal into a fraction, we can express it as an equation:
x = 16.666666667
Now, let's multiply both sides of the equation by 10 to eliminate the decimal:
10x = 166.66666667
Next, subtract the original equation from the new equation:
10x - x = 166.66666667 - 16.666666667
9x = 150
Now, divide both sides of the equation by 9:
9x/9 = 150/9
x = 16.666666667
By simplifying the fraction 16.666666667, we find that it equals 150/9.
Now, why is 150/9 an irrational number? It turns out that 150/9 is not an irrational number, but rather a rational number. It can be expressed as a fraction, where both the numerator and denominator are integers.
Therefore, 1.6666666667 is not an irrational number. It is a rational number because it can be written as the fraction 150/9.