A rational number always repeats itself?

Question

True or False????

Answer 1

False. A decimal that is a rational number may repeat, but it might also "terminate," or stop. For example, 0.13333.... with a repeating 3 IS a rational number, but so is 0.23 with no repeating.

Only decimals that neither repeat nor terminate are irrational.

**** Edit:

Just because it CAN be written as a repeating decimal doesn't mean it MUST. The question is whether a rational number ALWAYS repeats itself. Here's one that doesn't: 4.3

Here's another that doesn't: 0.005

If we can write a rational number that doesn't repeat itself, the answer is false.

Answer 2

True. This is so, because every rational, by definition, can be written as A/B where A,B belong to the Integers.

Even "terminating" decimals can be written as repeating decimals, without using repeated 0's. For example:

0.23 = 0.229999999999...
0.421 = 0.4209999999...
1 = 0.9999999999...

Answer 3

true.
note that it also can repeat with zero's as in 1.000000000...
.
any rational can be written as a fraction of two integers a/b , by carrying out the division you will see that the since ytou are working with integers and that there are only a finite number of integers ( namely those smaller than the divisor b ) , the decimal representation have to repeat.
.

Answer 4

True.

When rational numbers are written in decimal form, the digits following the decimal point will eventually begin to repeat.

Answer 5

Yes this is true

Answer 6

Shuck my balls