2007-07-26 03:40:16 · 12 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Sounds like you already knew the answer! You're right in saying that rational numbers can all be expressed in the form p / q where p and q are rational, so 22 / 7 is indeed rational. I'm assuming you're asking this question since 22 / 7 is an old estimation of pi, where pi itself is an irrational number?
2007-07-26 03:45:25 · answer #1 · answered by Bryan H 2 · 2⤊ 0⤋
YES, 22/7 is indeed a rational number, for the reason you stated.
This is a common APPROXIMATION for Ï, however it is not the ACTUAL value for Ï. Ï is an irrational number, and therefore there is no fraction that can express its exact value.
Brian D is incorrect when he says "It's irrational when you express it as a decimal". That's ridiculous. A rational number is a rational number. Another way of defining a rational number is to say that it's a decimal that either terminates or repeats. It turns out that all p/q numbers do this too. 22/7 is actually "3." followed by the sequence "142857" which keeps on repeating. Again, since pi is irrational, you can't write it as any string of numbers repeating. Nor do the decimals end.
2007-07-26 10:53:20 · answer #2 · answered by Anonymous · 0⤊ 1⤋
If you are specifically talking about the fraction 22/7, then yes it is a rational number. It is of the form p/q with p=22 and q=7. However, if you are confusing this with the value of pi, which is APPROXIMATELY 22/7, then no, pi is not a rational number. It is a nonterminating and nonrepeating decimal.
2007-07-26 10:56:32 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Yes 22/7 is a rational, and yes, you are correct that any thing of the form p/q where p and q are integers is rational.
I suppose the reason why your asking this is this numbers relation to pi. Pi is irrational so in order to get any solutions you have to have some approximation for it.
To be honest I don't know why this approximation is so popular, it is still an approximation and really no better, then any other.
2007-07-26 10:47:51 · answer #4 · answered by marvin0258 3 · 0⤊ 1⤋
Brian D is mistaken. The other answerers are correct.
A number is either rational or irrational now matter how it is expressed, fraction or decimal.
22/7 is rational, and it can be expressed as a decimal as 3.1428571428571428571428571428571..... if you really want to. It's still rational. Note the repeating term 142857. All rational numbers expressed as decimal have such repeating terms, or work out exactly.
Pi is irrational in that it cannot be accurately expressed as p/q, and neither can it be accurately expressed as decimal, only approximated: 3.14159265358979.... no repeating term here, it goes on for ever, seemingly randomly.
2007-07-26 10:58:06 · answer #5 · answered by Nick J 4 · 0⤊ 0⤋
yes and this is used as an approximation to pi note the word approximation.
sevenths look like they carry on forever (irrartional but infact they repeat every 6 decimal places
2007-07-26 10:47:35 · answer #6 · answered by JAMES C 2 · 0⤊ 1⤋
yes 22/7 a rational number,
but 3.14...... is not a rational number.
2007-07-26 10:43:35 · answer #7 · answered by ♫●GARV●♫ 6 · 0⤊ 2⤋
when pi is expressed as a fraction (22/7) it is rational ....
when 22/7 is expressed as a decimal, it no longer is rational...
the same value can be both rational & irrational.... depends how you express it.
2007-07-26 10:50:17 · answer #8 · answered by Brian D 5 · 0⤊ 4⤋
Yes.
2007-07-26 10:43:16 · answer #9 · answered by Becky M 4 · 0⤊ 1⤋
You have answered the question exactly as it should be answered and no further comment is required.
2007-07-26 13:20:25 · answer #10 · answered by Como 7 · 0⤊ 0⤋