Is .121221222122221... (the pattern in this number continues forever) a rational number or irrational number? Why?
(my research is listed in a previous question post, but I'm stuck!!! Please help!) :-)
Each term 0.12, 0.00122, 0.000001222, 0.00000000012222, ...
is a rational number. When continued forever and added together, it does not have to be a rational number.
Another example:
1, 1/3, 1/5, 1/7, 1/9, ... are all rational numbers.
If we look at the sum
S = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ....
S equals π/4, a known irrational number.
In fact, a non-recurring decimal number is considered an irrational number.
See:
http://en.wikipedia.org/wiki/Irrational_number
you have to put in the division,addition,sub., or whatever to answer this...(44,8,74,21,4)=10
Camy,
It is not a good idea to piggyback a question on someone else's question. It may get ignored or overlooked.
As there are no replies yet, I suggest you repost the question as a new thread.
Thank you.
To determine whether the number .121221222122221... is rational or irrational, let's break down the problem step by step.
1. Rational numbers: These are numbers that can be expressed as the ratio of two integers. Rational numbers can be written in the form p/q, where p and q are integers, and q is not equal to zero.
2. Irrational numbers: These are numbers that cannot be expressed as the ratio of two integers. Irrational numbers cannot be written in the form p/q, where p and q are integers, and q is not equal to zero.
In this case, the number .121221222122221... is a repeating decimal with a pattern that repeats indefinitely. To determine if it is rational or irrational, we need to convert it to fraction form.
Let's call the number x: x = .121221222122221...
Now, let's multiply x by a power of 10 to shift the decimal point:
10x = 1.21221222122221...
Next, subtract x from 10x to eliminate the repeating part:
10x - x = 1.21221222122221... - .121221222122221...
This simplifies to:
9x = 1.09099199990999...
Now, we can isolate x by dividing both sides of the equation by 9:
9x/9 = 1.09099199990999.../9
Simplifying further, we get:
x = 0.121221222122221...
Therefore, the number x is equal to the original number we started with.
Since x can be expressed as a fraction (x = 0.121221222122221...), we can conclude that the number .121221222122221... is a rational number.
In summary, .121221222122221... is a rational number because it can be expressed as the ratio of two integers.