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Is zero a rational number? Can you write it in the form, where p and q are integers and q ≠ 0?
Find five rational numbers between 1 and 2.
Find six rational numbers between 3 and 4.
Find five rational numbers between and .
Are the following statements true or false? Give reasons for your answer.
(i) Every whole number is a natural number.
(ii) Every integer is a rational number.
(iii) Every rational number is an integer.
(iv) Every natural number is a whole number.
(v) Every integer is a whole number.
(vi) Every rational number is a whole number
Express the following rational numbers as decimals:
(i) (ii) (iii)
(i) (ii) (iii) (iv) (v) (vi)
Look at several examples of rational numbers in the form (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating, decimal representations. Can you guess what property q must satisfy?
Express each of the following decimals in the form :
(i) 0.39 (ii) 0.750 (iii) 2.15 (iv) 7.010 (v) 9.90 (vi) 1.0001
(i) (ii) (iii) (iv) (v) (vi) (vii)
Define an irrational number.
Explain, how irrational numbers differ from rational numbers?
Examine, whether the following numbers are rational or irrational:
(i) (ii) (iii) 2+ (iv)
(v) (vi) (-2)2 (vii) (2-) (2+) (viii)
(ix) -2 (x) (xi) (xii) 0.3796 (xiii) 7.478478
(xiv) 1.101001000100001…..
Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:
(i) (ii) 3 (iii) (iv) (v) (vi)
In the following equations, find which variables x, y, z etc. represent rational or irrational numbers:
(i) x2 = 5 (ii) y2 = 9 (iii) z2 = 0.04 (iv) u2 = (v) v2 = 3 (vi) w2 = 27 (vii) t2 = 0.4
Give an example of each, of two irrational numbers whose:
(i) Difference is a rational number.
(ii) Difference is an irrational number.
(iii) Sum is a rational number.
(iv) Sum is an irrational number.
(v) Product is a rational number.
(vi) Product is an irrational number.
(vii) Quotient is a rational number.
(viii) Quotient is an irrational number.
Give two rational numbers lying between 0.232332333233332…. and 0.212112111211112.
Give two rational numbers lying between 0.515115111511115…. and 0.5353353335….
Find one irrational number between 0.2101 and 0.2222 ….= .
Find a rational number and also irrational number lying between the numbers 0.3030030003…..and 0.3010010001….
Find two irrational numbers between 0.5 and 0.55.
Find two irrational numbers lying between 0.1 and 0.12.
Prove that is an irrational number.
Find three different irrational numbers between the rational numbers and .
Complete the following sentences:
(i) Every point on the number line corresponds to a ….number which many be either …… or ……
(ii) The decimal from of an irrational number is neither……. nor…..
(iii) The decimal representation of a rational number is either ……… or ……….
(iv) Every real number is either …………… number or ……………. number.
Represent on the number line.
Represent on the real number line.
Find whether the following statements are true or false.
(i) Every real number is either rational or irrational.
(ii) π is an irrational number.
(iii) Irrational numbers cannot be represented by points on the number line.
Visualise 2.665 on the number line, using successive magnification.
Visualise the representation of on the number line up to 5 decimal places that is up to 5.37777.
Which one of the following is a correct statement?
Which one of the following statements is true?
Which of the following is a correct statement?
Which of the following statement is true?
Which of the following is irrational?
Which of the following is rational?
The number 0.318564318564318564……. is:
In n is a natural number, than is
Which of the following numbers can be represented as non-terminating, repeating decimals?
Every point on a number line represents
An irrational number between 2 and 2.5 is
The number of consecutive in 23×34×54× 7, is
The number in the form, where p and q are integers and q ≠ 0, is
The smallest rational number by which should be multiplied so that its decimal expansion terminates after one place of decimal, is
when expressed in the form (p, q are integers, q ≠ 0), is
The value of is
