Maths Rational and irrational Numbers Exercise1-3
Please Select
Q1 Locate √10 and √17 on the number line.
Q2 Write the decimal expansion of each of the following numbers and say what kind of decimal expansion each has:
(i) 36/100
(ii) 4 1/8
(iii) 2/9
(iv) 2/11
(v) 3/13
(vi) 329/400
Q3 Without actually performing the king division, State whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
(i) 13/3125
(ii) 17/8
(iii) 23/75
(iv) 6/15
(v) 1258/625
(vi) 77/210
Q4 Without actually performing the long division, find if 987/10500 will have terminating or non-terminating repeating decimal expansion. Give reasons for your answer.
Q5 Write the decimal expansions of the following numbers which have terminating decimal expansions:
(i) 17/8
(ii) 13/3125
(iii) 7/80
(iv) 6/15
(v) 2²×7/54
(vi) 237/1500
Q6 Write the denominator of the rational number 257/5000 in the form 2 m × 5 n> where m, n is non-negative integers. Hence, write its decimal expansion on without actual division
Q7 Write the decimal expansion of 1/7. Hence, write the decimal expression of?
2/7, 3/7, 4/7, 5/7 and 6/7.
Q8 Express the following numbers in the form p/q’. Where p and q are both integers and q≠0;
Q9 Classify the following numbers as rational or irrational:
(i) √23
(ii) √225
(iii) 0.3796
(iv) 7.478478
(v) 1.101001000100001…
Q10 The following real numbers have decimal expansions as given below. In each case, state whether they are rational or not. If they are rational and expressed in the form p/q, where p, q are integers, q≠ 0 and p, q are co-prime, then what can you say about the prime factors of q?
(i) 37.09158
(iii) 8.9010010001…
(iv) 2.3476817681…
Q11 Insert an irrational number between the following.
(i) 1/3 and ½
(ii) -2/5 and ½
(iii) 0 and 0.1
Q12 Insert two irrational numbers between 2 and 3.
Q13 Write two irrational numbers between 4/9 and 7/11.
Q14 Find one rational number between √2 and √3
Q15 Find two rational numbers between 2√3 and √15.
Q16 Insert irrational numbers between √5 and √7.
Q17 Insert two irrational numbers between √3 and √7.
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