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A number in the form of a ratio a /b, where a and b are integers , and b is not equal to 0, is called a rational number. The rational numbers are a subset of the real numbers, and every rational number can be expressed as a fraction or as a decimal form that either terminates or repeats. Conversely, every decimal expansion that either terminates or repeats represents a rational number. Rational numbers can be written in several different forms using equivalent fractions. For example, . There are an infinite number of ways to write 1, Â¼ or by multiplying both the numerator and denominator by the same nonzero integer. Therefore, there are an infinite number of ways to write every rational number in terms of its equivalent fraction. The following example shows how to find the ratio of integers that represents a repeating decimal. One way to compare two rational numbers is to convert them into a decimal form. Dividing the numerator by the denominator results in the decimal equivalent. If the division has no remainder, then the decimal is called a terminating decimal. For example, Â½ = 0.5, , and . Although some decimals do not terminate, they do repeat because at some point a digit, or group of digits, repeats in a regular fashion. Examples of repeating decimals are â…“ = 0.333â€¦,, and . A bar written over the digits or group of digits that repeat shows that the decimal is repeating: , and . Rational numbers satisfy the following properties. see also Integers; Numbers, Irrational; Numbers, Real; Numbers, Whole. Rafiq Ladhani Amdahl, Kenn, and Jim Loats. Algebra Unplugged. Broomfield, CO: Clearwater Publishing Co., 1995. Miller, Charles D., Vern E. Heeren, and E. John Hornsby, Jr. Mathematical Ideas, 9th ed. Boston: AddisonWesley, 2001.
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Answers:So you are absolutely correct. but as you said rational numbers can be written in a fraction which is not the correct definition. In a fraction we get only positive numbers. But in a rational number we get positive as well as negative integers. for ex; 3/7, 4/5, 4/5 here you should also remember that all fractions are rational numbers but all rational numbers are not fractions. A number which can be expressed in the p/q form where p and q are integers and q is not equal to zero is called a rational number. all others are irrational numbers. and as you said the set of rational and irrational together are called real numbers. hope it is clear to you.
Answers:i don't know which standard you are studying remember one thing all integers are rational nos example 1, 23, 765, 38342476 etc but not all fractions are also rational nos there are two kinds of fractions which are considered to be rational no 1. terminating decimals eg: 1/4= 0.25 the division is perfect and terminating 2. non terminating decimals but with repeated patterns eg1: 10/3 = 3..3333333 which is non terminating but the 3 after decimal is repeating eg2: 45/7 = 6.428571428571428571428571428571 ..... here we find the digits 428571 is repeated infinite times these are rational nos the third kind which goes into irrational no is one which don't have terminating and non repeated pattern eg: 7.423 345 123 765 ....... but the pattern after decimal don't repeat and the division is never complete so such nos are said to be irrational nos but 22/7 is a rational no But if you consider 22/7 as the approximation of PI(mathematical symbol) then it is irrational because as i said approximation is rational but real pi is irrational hope i cleared your doubt if you have still doubt refer some NCERT text books of 9th and 10th standardstandard
Answers:youre right about the definitions .72222222222= .7  .02222222 .7 = 7/10 .022222222 = .222222222 * (1/10) = 2/9 * 1/10 = 2/90 so .722222222 = 7/10  2/90 = 63/90  2/90 = 65/90 = 13/18
Answers:Irrational number is basically a number that cannot be expressed in fraction form, with both denominator and numerator as integers. EG: Square root of 3 4 is rational since it can be expressed as 4/1. the 5 blah blah and 1.37 blah blah are irrational, since they cannot be expressed in fraction form.