5/7 is rational because it is the fraction of two integers. As far as the decimal for 5/7, the decimal for any rational number must either end or have a repeating block of numbers. It sure looks like the decimal for 5/7 doesn't end! And it's a big tough to see with a normal calculator, but it does have a repeating block of decimals. It goes like this 0.714285714285714285714285714285714285... crazy! Actually all the 7th repeat in a block of 6 numbers. 1/7 = 0.142857142857142857142857142857142857... Now on my calculator screen 1/7 says 0.1428571429. The 9 at the end is there because my calculator is rounding up. There is actually no 9 in the decimal for 1/7.
MrCaryMath . Thanks for the reply....I have since learned that there is a way of determining whether the 'ratio' is rational using a method of primes, without having to see if a decimal only repeats after an inordinate number of places.
nice & clear examples......the video helped.....thanks......
Thank you. This was very helpful and very clear! Apreciated.
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Glad the video helped!
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MrCaryMath. So 5/7 is irrational ! It's the division of two integers...yet equals 0.714285714........ Please clarify.
5/7 is rational because it is the fraction of two integers. As far as the decimal for 5/7, the decimal for any rational number must either end or have a repeating block of numbers. It sure looks like the decimal for 5/7 doesn't end! And it's a big tough to see with a normal calculator, but it does have a repeating block of decimals. It goes like this 0.714285714285714285714285714285714285... crazy! Actually all the 7th repeat in a block of 6 numbers. 1/7 = 0.142857142857142857142857142857142857... Now on my calculator screen 1/7 says 0.1428571429. The 9 at the end is there because my calculator is rounding up. There is actually no 9 in the decimal for 1/7.
MrCaryMath . Thanks for the reply....I have since learned that there is a way of determining whether the 'ratio' is rational using a method of primes, without having to see if a decimal only repeats after an inordinate number of places.
Thank you!
Very good vid.
If u think ur smart give thumbs up! :D
Thank you!