Which number is a rational, terminating decimal?(1 point)

Question

Responses

0.363636...
0.363636...

79
7 ninths

64−−√
square root of 64

511
5 over 11

Answer 1

The number 5 over 11 is a rational, terminating decimal.

Answer 2

how is it terminating when the answer repeat

Answer 3

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.

Answer 4

but how is 0.363636 a terminating decimal and not the square root of 64?

Answer 5

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.