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HOLIDAY HOMEWORK

SUBMITTED BY-LAKSHMI SINGH

SUBMITTED TO-

2INDEX

• RATIONAL NUMBERS• IRRATIONAL NUMBERS

3RATIONAL NUMBERS

A rational number is a number that can be written in the form p/q , where p and q are integers and q is not equal to 0. EXAMPLES- 2/5, -3/4

The collection of numbers in the form of p/q, where q ≠ 0, is represented by Q.

Rational numbers include natural numbers, whole numbers, integers and all negative and positive fractions.

4TYPES OF RATIONAL NUMBERS

Positive rational numberRational number is positive if its numerator and denominator are both either positive integers or negative integers. Eg : 2/5 , -8/-5.Negative rational numberIf either the numerator or the denominator of a rational number is a negative integer ,then the rational number is called a negative rational number. Eg: -2/5Standard formA rational number is said to be in its standard form if its numerator and denominator have no common factor other than 1,and its denominator is a positive integer . Eg: 4/7

5Representation of Rational Numbers on the Number Line

To express rational numbers appropriately on the number line, divide each unit length into as many number of equal parts as the denominator of the rational number and then mark the given number on the number line.

6OPERATION ON RATIONAL NUMBERS

1. ADDITION OF RATIONAL NUMBERSTo add rational numbers that have a common denominator, we add the numerators, but we do not add the denominators

NOTE: To add rational numbers that have a common denominator, we add the numerators, but we do not add the denominators

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2. SUBTRACTION OF RATIONAL NUMBERSSubtraction is the inverse operation of addition. To subtract rational numbers that have a common denominator, we subtract the numerator, but we do not subtract the denominators.

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3. MULTIPLYING TWO RATIONAL NUMBERSTo multiply two rational numbers, we multiply the numerators to get the new numerator and multiply the denominators to get the new denominator

4. DIVISION OF TWO RATIONAL NUMBERS

9IRRATIONAL NUMBERS

An irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers, with b non-zero, and therefore not a rational number.

All numbers which cannot be written as an integer upon integer where the denominator is zero and both integers are co-primes are irrational numbers.

They are non - terminating non-repeating decimal expansions.

The roots of prime number are irrational.

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EXAMPLES OF IRRATIONAL NUMBERS = 3.1415926535897932384626433 e= 2.71828182845904523536 =1.41421356237309504 =1.732050807568877293527

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