Which number is a rational, terminating decimal?(1 point)
Responses
0.363636...
0.363636...
79
7 ninths
64−−√
square root of 64
511
5 over 11
5 answers
The number 5 over 11 is a rational, terminating decimal.
how is it terminating when the answer repeat
Apologies for the confusion. You are correct.
In this case, the number 0.363636... is a rational number that represents a repeating decimal. A repeating decimal implies that there is a pattern of digits that repeats indefinitely. In this case, the pattern is "36".
To find a rational number equivalent to this repeating decimal, you can set up an equation:
Let x = 0.363636...
Then, multiplying both sides of the equation by 100, we get:
100x = 36.363636...
Now, we can subtract the original equation from this equation to eliminate the repeating part:
100x - x = 36.363636... - 0.363636...
99x = 36
Therefore, x = 36/99, which simplifies to 4/11.
So, the rational number equivalent to 0.363636... is 4/11, which is a terminating decimal.
In this case, the number 0.363636... is a rational number that represents a repeating decimal. A repeating decimal implies that there is a pattern of digits that repeats indefinitely. In this case, the pattern is "36".
To find a rational number equivalent to this repeating decimal, you can set up an equation:
Let x = 0.363636...
Then, multiplying both sides of the equation by 100, we get:
100x = 36.363636...
Now, we can subtract the original equation from this equation to eliminate the repeating part:
100x - x = 36.363636... - 0.363636...
99x = 36
Therefore, x = 36/99, which simplifies to 4/11.
So, the rational number equivalent to 0.363636... is 4/11, which is a terminating decimal.
but how is 0.363636 a terminating decimal and not the square root of 64?
Apologies for the confusion in my previous response.
You are correct, 0.363636... is not a terminating decimal, but a repeating decimal.
The square root of 64 is 8, which is a rational number, and therefore a terminating decimal.
You are correct, 0.363636... is not a terminating decimal, but a repeating decimal.
The square root of 64 is 8, which is a rational number, and therefore a terminating decimal.