For example, if we take the number 178564, the last two digits form 64 since the number 64 is divisible by 4 the number 178564 is divisible by 4. Hence the number 74549 is not divisible by 3.ĭivisibility by 4: A number is divisible by 4 if the number formed with its last two digits is divisible by 4. If we take the number 74549, the sum of the digits is 29 which is not a multiple of 3. Similarly 342, 789 etc are all divisible by 3. Hence, the given number 9123 is divisible by 3. We will look at some rules for divisibility of numbers.ĭivisibility by 2: A number divisible by 2 will have an even number as its last digit ( For example 128, 246, 2346 etc)ĭivisibility by 3: A number is divisible by 3 if the sum of its digits is a multiple of 3.įor example, take the number 9123, the sum of the digits is 9 + 1 + 2 + 3 = 15 which is a multiple of 3. Some of the factors of a given number can, in a number of situations, be found very easily either by observation or by applying simple rules. In a number of situations, we will need to find the factors of a given number.
Numbers like π, ε are also irrational numbers.īetween any two numbers, there are infinite numbers of irrational numbers.Īnother way of looking at rational and irrational numbers isĪny terminating or recurring decimal is a rational number.Īny non – terminating non – recurring decimal is an irrational number. Examples for irrational numbers are √2,√3,∜5, ∛8etc. Numbers which are not rational but which can be represented by points on the number line are called irrational numbers. We will study in another section in this chapter the way to convert recurring decimals into fractions.īetween any two numbers, there can be infinite number of other rational numbers. Any recurring decimal can be expressed as a fraction of the form p/q and hence it is a rational number. A recurring decimal is a number in which one or more digits at the end of a number after the decimal point repeats endlessly ( For example, 0.333…., 0.111111…, 0.166666…., etc.
Recurring decimals are also rational numbers. Real Number are classified into rational and irrational numbers.Ī number which can be expressed in the form p/q where p and q are integers and q ≠ 0 is called a rational number.įor example, 4 is a rational number since 4 can be written as 4/1 where 4 and 1 are integers and the denominator 1≠0.
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