Which number is a rational, terminating decimal?(1 point)Responses5115115 over 1164−−√64square root of 640.363636...0.363636...79
3 answers
The rational, terminating decimal in the options given is 0.363636...
how
The decimal 0.363636... is a rational, terminating decimal because it can be expressed as a fraction. To determine the fraction equivalent of this repeating decimal, we can assign it to a variable, let's say x.
x = 0.363636...
Now, we can multiply both sides of the equation by 100 to eliminate the repeating decimal:
100x = 36.363636...
Next, we subtract the original equation from the multiplied equation:
100x - x = 36.363636... - 0.363636...
99x = 36
Lastly, we divide both sides of the equation by 99 to solve for x:
x = 36/99
Therefore, the number 0.363636... is equivalent to the rational number 36/99 or 4/11.
x = 0.363636...
Now, we can multiply both sides of the equation by 100 to eliminate the repeating decimal:
100x = 36.363636...
Next, we subtract the original equation from the multiplied equation:
100x - x = 36.363636... - 0.363636...
99x = 36
Lastly, we divide both sides of the equation by 99 to solve for x:
x = 36/99
Therefore, the number 0.363636... is equivalent to the rational number 36/99 or 4/11.
1 answer