Is PI A Rational Number Is PI A Rational Number
Let us remind the concept of Rational Numbers. Rational numbers are the ratio of two different unified integers. Or in other words, we can say that rational numbers are simply the ratio of two numbers with no common factor in them. Now, any fractional number may be a rational number or may not be, it depends on the nature of the fractional number that is whether the number has finite number after decimal or not. If any fractional number is re-written as the simplified ratio then it is a rational number. Let us remind the concept of Rational Numbers. Rational numbers are the ratio of two different unified integers. Or in other words, we can say that rational numbers are simply the ratio of two numbers with no common factor in them. Now, any fractional number may be a rational number or may not be, it depends on the nature of the fractional number that is whether the number has finite number after decimal or not. Know More About Associative Property Worksheets
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If any fractional number is re-written as the simplified ratio then it is a rational number. Pi is irrational. There is no unit of length no matter how small that the circumference of any circle and it's diameter can be divided up by to set up the ratio C / D where C and D are integers. Since Pi = C / D it is irrational and it's decimal representation is non repeating and non terminating to the right of the decimal point. All rational numbers can be represented exactly as a ratio of integers or, equivalently, as a "repeating" decimal. For example, one half is rational since it can be expressed exactly as either 1/2 or as 0.5000000.... where 0 repeats to Infinity. Likewise one third is rational since it can expressed exactly as 1/3 or as 0.333333..... where 3 repeats to infinity. Pi is not a rational number. Although it can be closely approximated by such values as 22/7 (3 1/7) they are only approximations and are not the exact value of pi. The value of pi has been calculated out to a trillion (10^12) decimal places and no sequence of digits repeats. That is indicative that pi is irrational, but is not not a proof. Since the value of pi that is also written as ( 22 / 7 ) but this value is not perfect that is it is an approximate value, the actual value of pi is 3.14159265 and it is an non – terminating number, there fore pi is not an rational number. Irrespective of the value of pi that is 22/7 it is not considered as a rational number as the actual value of pi is 3.14159265 which is not a rational number. Therefore the number pi is not a rational number. Read More About Verifying Trigonometric Identities Worksheet
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Irrational number is a number that cannot be written as a fraction a/b where a and b are integer numbers, with b different of zero. In practical way, it is a decimal number with infinity digits without formal repetition... There are some famous irrational numbers as: pi = 3.141592... , e = 2,71828... And Other by square root not exact as: sqrt(2) = 1.414113... , sqrt(3) =1.732050... , sqrt(5) ... But you can write a irrational number... just write a fraction with infinity digits, without formal repetition... Example: 7,12345678910111213... or -15,01001000100001000001... If the digits have a formal repetition, then it is not a rational, because can be written as a fraction, Example: 2.777777777... = 2(7/9) or 0.52525252525252... = 52/99 or 0.5555555... = 5/9 OK!
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