Mathematics 9th - Exercise 1.1 REAL AND COMPLEX NUMBERS

Mathematics 9th - Exercise 1.1 REAL AND COMPLEX NUMBERS

  1. Identify the following numbers as rational and irrational numbers and also write each one in separate column.

(i) 15\frac{1}{5}
Solution:
15=0.2\frac{1}{5} = 0.2 = Rational Number

(ii) 28\frac{\sqrt{2}}{8}​

Solution:
28=1.414218=0.176776  Irrational Number

(iii) 56\frac{5}{\sqrt{6}}
Solution:
56=52.4494=2.041316  Irrational Number

(iv) 28\frac{2}{8}
Solution:
28=0.25\frac{2}{8} = 0.25 = Rational Number

(v) 13\frac{1}{\sqrt{3}}

Solution:

13=11.73205=0.577350 Irrational Number

(vi) 8\sqrt{8}
Solution:
8=2.82842​ Irrational Number

(vii) ee
Solution:
e=2.718281 Irrational Number

(viii) π\pi
Solution:
π=227=3.1428…\pi = \frac{22}{7} = 3.1428\ldots = Irrational Number

(ix) 5\sqrt{5}
Solution:
5=2.23606 Irrational Number

(x) 223\frac{22}{3}
Solution:
223=7.3333Rational Number

(xi) 1π\frac{1}{\pi}
Solution:
1π=13.14=0.3184 Irrational Number

(xii) 1112\frac{11}{12}
Solution:
1112=0.91666 Irrational Number

2. Convert the following into decimal fractions. Also indicate them as terminating and non-terminating decimal fractions.

(i) 58\frac{5}{8}
Solution:
58=0.625\frac{5}{8} = 0.625Terminating decimal fraction

(ii) 418\frac{4}{18}
Solution:
418=0.2222 Non-terminating decimal fraction

(iii) 115\frac{1}{15}
Solution:
115=0.06666\frac{1}{15} = 0.06666Non-terminating decimal fraction

(iv) 498\frac{49}{8}
Solution:
498=6.125\frac{49}{8} = 6.125 Terminating decimal fraction

(v) 20715\frac{207}{15}
Solution:
20715=13.8\frac{207}{15} = 13.8 Terminating decimal fraction

(vi) 5076\frac{50}{76}
Solution:
5076=0.6578 Non-terminating decimal fraction

3. Represent the following rational numbers on the number line.

(i) 810\frac{8}{10}
Solution:
810=0.8\frac{8}{10} = 0.8

(ii) −810\frac{-8}{10}
Solution:
−810=−0.8\frac{-8}{10} = -0.8

(iii) 1141 \frac{1}{4}
Solution:
114=54=1.251 \frac{1}{4} = \frac{5}{4} = 1.25

(iv) −114-1 \frac{1}{4}
Solution:
−114=−1.25-1 \frac{1}{4} = -1.25

(v) 23\frac{2}{3}
Solution:
23=0.666\frac{2}{3} = 0.666

(vi) −23\frac{-2}{3}
Solution:
−23=−0.666\frac{-2}{3} = -0.666

4. Can you make a list of all rational numbers between 1 and 2?

Solution:
(i) 32=1.5\frac{3}{2} = 1.5
(ii) 54=1.25\frac{5}{4} = 1.25
(iii) 98=1.125\frac{9}{8} = 1.125
(iv) 74=1.75\frac{7}{4} = 1.75

5. Give a reason why π\pi is an irrational number?

Solution:
π=227=3.14285...\pi = \frac{22}{7} = 3.14285...
Pi (π\pi) is an irrational number because it is non-terminating and non-recurring decimal.

6. Tick (✓\checkmark) the correct statements.

(i) 57\frac{5}{7} is an example of an irrational number. ✓\checkmark
(ii) π\pi is an irrational number. ✓\checkmark
(iii) 0.3159... is an example of non-terminating and non-repeating decimal fraction. ✓\checkmark
(iv) 0.1230.123 is an example of a recurring decimal fraction. ×\times
(v) 12,13\frac{1}{2}, \frac{1}{3}are lying between 0 and 1. ✓\checkmark
(vi) 13\frac{1}{\sqrt{3}}is an example of a rational number. ×\times

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