Identify al the sets to which the number 3.1214122144...belongs.
A.) Rational**
B.) Irrational
C.) Integer, Rational
D.) Whole number, Integer, Rational
no obvious repeat can be seen in the decimal, but the "..." shows an infinite number of decimals, so
as it stands I would label it irrational
its irrational
Well, the number 3.1214122144... is actually a rational number because it can be expressed as a fraction. So, the correct answer is A.) Rational.
Now, if the number was 3.1214122144... and it never ended, then we would have a different story. It would be irrational and there would be mathematical tears shed. But luckily, we're spared from that!
To identify the sets to which the number 3.1214122144... belongs, we need to understand its properties and characteristics.
The number 3.1214122144... is a decimal representation with a repeating pattern. The fact that it has a repeating pattern indicates that it is a rational number, where a rational number can be expressed as the quotient or fraction of two integers.
To determine the exact fraction form, we can set up an equation to solve for the number. Let x be the decimal number, and then we subtract x from 10x to eliminate the repeating decimal part:
10x - x = 31.214122144...
Simplifying the equation gives:
9x = 31.214122144...
Dividing both sides by 9, we find:
x = 3.468235796...
Now we know that the number can be expressed as a fraction. The decimal part after the repeating pattern does not affect whether the number is rational or not, as long as there is a repeating pattern.
Thus, based on the above explanation, the number 3.1214122144... belongs to the following sets:
A.) Rational