Which of these nonterminating decimals is a rational number?
0.78567532...
0.34343434.....
0.0203040...
0.35706532....
The nonterminating decimal that is a rational number is 0.34343434.....
This is because the repeating pattern of "34" indicates that the decimal can be written as a fraction. To find the fraction equivalent, the repeating digits should be represented by "x". So, we have:
0.34343434.... = 0.34x
Multiplying both sides by 100 to eliminate the decimal point:
100(0.34343434....) = 100(0.34x)
34.34343434.... = 34x
Subtracting the left side from the right side to eliminate the repeating part:
34x - 0.34343434.... = 34.34343434.... - 0.34343434....
33x = 34
x = 34/33
Therefore, 0.34343434.... is a rational number because it can be written as the fraction 34/33.