Which is irrational?
A. 0.117117117...
B. 0.8596873205...
C. 0.812812812812...
D. 0.605605605...
Is the answer B?
OMG These responses were from 2014?!!! OMG SLAY
A, C, and D show a definite pattern of repetition, so they are rational
B ??? hard to tell , perhaps there is a repetition further down
I suspect the want you to say B
Ah, irrational numbers, such an emotionally unpredictable bunch! But fear not, my friend! We're not discussing your Aunt Mildred's dating history here. When it comes to mathematical irrationality, we're talking about numbers that can't be expressed as fractions. Now let's address your question. You've made quite the logical...or perhaps irrational...guess. But in this case, B is not the correct answer. Any other guesses?
To determine which number is irrational, we need to check if the decimal expansion of each number repeats or terminates.
Option A: 0.117117117...
The decimal expansion of A repeats the pattern "117". Therefore, this number is rational.
Option B: 0.8596873205...
The decimal expansion of B does not repeat or terminate, which means it goes on indefinitely. Therefore, this number is irrational.
Option C: 0.812812812812...
The decimal expansion of C repeats the pattern "812". Therefore, this number is rational.
Option D: 0.605605605...
The decimal expansion of D repeats the pattern "605". Therefore, this number is rational.
Thus, the correct answer is B.
To determine which number is irrational among the given options, we need to understand what it means for a number to be irrational.
An irrational number is any real number that cannot be expressed as a fraction or the ratio of two integers. These numbers have non-repeating and non-terminating decimal representations.
Now, let's examine each option:
A. 0.117117117...
This number is a repeating decimal, specifically with the repeating pattern "117." Repeating decimals can be rational, so this is a rational number.
B. 0.8596873205...
The decimal representation of this number does not exhibit a clear repeating or terminating pattern. However, without further information about the number's nature, we cannot definitively conclude whether it is rational or irrational.
C. 0.812812812812...
Similar to option A, this number has a repeating pattern, namely "812." Hence, it is also a rational number.
D. 0.605605605...
Once again, this number has a repeating pattern of "605." Therefore, it is a rational number.
Based on the analysis, none of the given options can be definitively identified as irrational. Hence, the answer cannot be determined with the information provided.