which of the non terminating decimals can be converted into a rational number.
A. 0.818118111...
B. 0.20304050...
C. 0.10110111...
D. 0.321321321...
I only see one choice which has repeating patterns.
Study this site.
https://www.mathsisfun.com/rational-numbers.html
Try each of those choices. What do you think?
i think that the answer is d
It has to be D because the rest are all different but that's the only one that is different.
the three dots mean that the decimal keeps going on
To determine which of the given non-terminating decimals can be converted into a rational number, we need to understand the concept of a rational number.
A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. Any number that can be written in the form p/q, where p and q are integers, and q is not zero, is a rational number.
Let's analyze each option to determine if it can be a rational number:
A. 0.818118111...
To convert this decimal into a fraction, we can assign it the variable x. Thus, we have:
x = 0.818118111...
Multiplying both sides by 1000 to move the decimal point, we get:
1000x = 818.118111...
Subtracting the original equation from this equation, we get:
1000x - x = 818.118111... - 0.818118111...
Simplifying, we have:
999x = 817.3
Dividing both sides by 999, we find:
x ≈ 0.818499...
Since this decimal is not repeating, it cannot be expressed as a fraction of two integers. Therefore, option A is not a rational number.
B. 0.20304050...
Similar to above, let's assign the variable x to this decimal:
x = 0.20304050...
Multiplying both sides by 10000000 to move the decimal point, we get:
10000000x = 20304050.05000000...
Subtracting the original equation from this equation, we get:
10000000x - x = 20304050.05000000... - 0.20304050...
Simplifying, we have:
9999999x = 20304049.8479595...
Dividing both sides by 9999999, we find:
x ≈ 2.0304049865...
Since this decimal is also not repeating, it cannot be expressed as a fraction of two integers. Therefore, option B is not a rational number.
C. 0.10110111...
Assigning the variable x to this decimal:
x = 0.10110111...
Multiplying both sides by 10000 to move the decimal point, we get:
10000x = 1011.0111...
Subtracting the original equation from this equation, we get:
10000x - x = 1011.0111... - 0.10110111...
Simplifying, we have:
9999x = 1010.90998888...
Dividing both sides by 9999, we find:
x ≈ 0.1011
This decimal is repeating, with the pattern "1011" repeating. Hence, it can be expressed as a fraction of two integers, making option C a rational number.
D. 0.321321321...
Assigning the variable x to this decimal:
x = 0.321321321...
Multiplying both sides by 1000 to move the decimal point, we get:
1000x = 321.321321...
Subtracting the original equation from this equation, we get:
1000x - x = 321.321321... - 0.321321321...
Simplifying, we have:
999x = 321
Dividing both sides by 999, we find:
x ≈ 0.321
This decimal is not repeating and can be expressed as a fraction of two integers. Therefore, option D is a rational number.
In conclusion, the non-terminating decimal that can be converted into a rational number is option D.