Is The number 0.8555555555555555 rational or irrational
The number 0.8555555555555555 is a rational number.
The number 0.8555555555555555 is a rational number. A rational number is any number that can be expressed as a quotient or fraction of two integers, where the denominator is not zero. Since the number 0.8555555555555555 can be written as 77/90, it is rational.
To determine if a number is rational or irrational, we need to understand what these terms mean.
A rational number is a number that can be expressed as a fraction, where the numerator and denominator are both integers (whole numbers), and the denominator is not zero.
An irrational number, on the other hand, cannot be expressed as a simple fraction. It is a number that cannot be expressed as a ratio of two integers.
Now, let's consider the number 0.8555555555555555. To determine if it's rational or irrational, we need to examine its decimal representation.
It's evident that the number has a repeating pattern of 5's. In decimal representation, a repeating pattern indicates that the number can be expressed as a fraction.
To find the fraction, we can represent the repeating decimal as x, subtract it from the original number, and then multiply it by a power of 10 in order to eliminate the repeating part. Let's denote the original number as N and the repeating part as x.
N = 0.8555555555555555
x = 0.8555555555555555
N - x = 0.8555555555555555 - 0.8555555555555555 = 0
Now, let's multiply N - x by 10 raised to the power of the number of digits in x, which in this case is 16:
(N - x) * 10^16 = 10^16 * 0
This gives us:
10^16N - 10^16x = 0
10^16N = 10^16x
Dividing both sides by 10^16, we have:
N = x
This implies that the original number N is equal to the repeating part x.
Since x can be expressed as a fraction (x = 8555555555555555 / 10^16), it follows that the number N (0.8555555555555555) is a rational number.
Therefore, the answer to your question is that the number 0.8555555555555555 is rational.