Is 14/3 a rational number? I think so... but I'm confused because if you divide 14 by 3 then the decimal part is .66666666666666666666667. Is that considered a repeating decimal? If it is, then it's a rational number. I'm just doubting because of the 7 at the end. THANKS SO MUCH!!! =D
yes it is a rational number since it can be written as a fraction, or a RATIO.
nothing to be confused about.
Your calculator has a build-in function which rounds off the last decimal it can display, that's why it shows up as a 7
When you do a long division, the way it was taught to you in earlier grades, the 6 will keep on repeating forever.
So is it a national number or what?
I meant rational, so sorry.
thank you so muchhhhhhhh. =]
Ah, not to beat a dead horse here but let's make sure the cart is before that horse. The real point is that 14/3 is a RATIO of whole numbers as Reiny capitalized.
That is what makes it a rational number.
The fact that it is a repeating decimal means that it can be written as a ratio, and therefore is rational.
In other words
If ratio, then rational
If repeating decimal, then ratio
Therefore
If repeating decimal, then rational
I suspect shortly you will be shown how to find the ratio that corresponds to any repeating decimal.
Yes, 14/3 is indeed a rational number. A rational number is any number that can be expressed as a fraction, where both the numerator and the denominator are integers.
To determine if 14/3 is a rational number, we need to check if the decimal representation is a repeating decimal or a terminating decimal.
When you divide 14 by 3, you get a decimal representation of 4.66666666666667. You are correct that the decimal part repeats with the digits 6, but there is a 7 at the end.
In mathematics, a repeating decimal is a decimal representation where one or more digits repeat indefinitely. In the case of 4.66666666666667, the repetition is characterized by the digit 6. The 7 at the end of the decimal does not affect the classification of the number as a repeating decimal.
Therefore, since 14/3 has a repeating decimal representation, it is considered a rational number.