1Mark each statement right (√) or wrong (×): (a) The set of real numbers contains all rational and all irrational numbers. (b) The set of rational numbers and the set of irrational numbers are disjoint sets. (c) The set of whole numbers and the set of integers are the same. (d) \( Z \subset Q \subset R \) (e) \( \sqrt{4} \) is irrational. (f) \( Z \supset N \supset W \) (g) Every rational number is a real number.Show Answer

2Say whether each number is rational or irrational, and why: \( \frac{3}{4} \), \( \sqrt{2} \), \( \sqrt{5} \), \( \frac{2}{5} \), \( \frac{10}{20} \), 3.57, 3.5982…, \( -15 \), 0.735…, \( -\sqrt{169} \), \( \sqrt{3} \), \( \sqrt{26} \), \( 2.\overline{5} \), \( \frac{35}{9} \), \( \sqrt[3]{9} \).Show Answer

3Change these decimals into fractions: \( 0.\overline{5} \), \( 0.\overline{7} \), \( 0.\overline{24} \), \( 0.\overline{132} \), \( 0.\overline{27} \), \( 1.\overline{57} \), \( 0.\overline{365} \), \( 4.\overline{78} \), \( 0.\overline{445} \), \( 1.\overline{525} \).Show Answer

4Show these numbers on the number line: \( \sqrt{5} \), \( \sqrt{6} \), \( \sqrt{7} \), \( \sqrt{8} \).Show Answer

5Define rational and irrational numbers with examples.Show Answer

6Show the relationship between rational and irrational numbers in a Venn diagram.Show Answer

7Write two differences between rational and irrational numbers.Show Answer

8Write these numbers in scientific notation: 45, 3400, 0.000023, 101000, 0.010, 45.01, 7000000, 0.00671, 625.6, 0.07882, 118000, 87200, 0.00000272, 0.000037, 74171.7, 3456.78.Show Answer

9Change these into ordinary decimal numbers: \( 2.30 \times 10^{4} \), \( 5.40 \times 10^{1} \), \( 1.76 \times 10^{0} \), \( 1.76 \times 10^{-3} \), \( 7.4 \times 10^{-5} \), \( 1.901 \times 10^{-7} \), \( 1.525 \times 10^{6} \), \( 6.58157 \times 10^{7} \), \( 5.256 \times 10^{8} \), \( 5.23 \times 10^{-7} \), \( 8.71 \times 10^{-8} \), \( 7.75763 \times 10^{-9} \).Show Answer

10A loaded truck weighs 12,000 kg. Write this weight in scientific notation.Show Answer

11The radius of an argon atom is 0.000,000,000,098 metre. Write it in scientific notation.Show Answer

12The speed of light in air is \( 3 \times 10^{8} \) m/s. What is this as an ordinary number? Also, the speed of light is about 3,00,000 km/s; write that in scientific notation.Show Answer

13A month of 30 days has 6,480,000 seconds. What is this in scientific notation?Show Answer

14A fuel depot in Kathmandu is holding \( 1.87 \times 10^{6} \) litres of petrol. How many kilolitres is that?Show Answer

15Simplify and give the answer in scientific notation: \( (1.2 \times 10^{5}) + (5.35 \times 10^{6}) \), \( 6.91 \times 10^{-2} + 2.4 \times 10^{-3} \), \( 9.70 \times 10^{6} + 8.3 \times 10^{5} \), \( 3.67 \times 10^{2} - 1.6 \times 10^{1} \), \( 8.41 \times 10^{-5} - 7.00 \times 10^{-6} \), \( 1.33 \times 10^{5} - 4.9 \times 10^{4} \).Show Answer

16Simplify and give the answer in scientific notation: \( (4.3 \times 10^{8}) \times (2.0 \times 10^{6}) \), \( (6.0 \times 10^{3}) \times (1.5 \times 10^{-2}) \), \( (1.5 \times 10^{-2}) \times (8.0 \times 10^{-1}) \), \( (5.23 \times 10^{11}) \times (3.0 \times 10^{-10}) \), \( \frac{1.20 \times 10^{-8}}{3.0 \times 10^{-3}} \), \( \frac{7.8 \times 10^{-12}}{1.3 \times 10^{-13}} \), \( \frac{8.4 \times 10^{-4}}{1.2 \times 10^{-3}} \), \( \frac{5.6 \times 10^{-18}}{1.4 \times 10^{-8}} \), \( \frac{8.1 \times 10^{9}}{9.0 \times 10^{8}} \), \( \frac{3.25 \times 10^{-10}}{1.625 \times 10^{-15}} \).Show Answer

17Simplify: \( \frac{(1.1 \times 10^{3}) + 2.3 \times 10^{3}}{1.7 \times 10^{-6}} \) and \( \frac{9.8 \times 10^{8} - 4.9 \times 10^{8}}{7.0 \times 10^{7}} \).Show Answer

18Simplify: \( \frac{(2.1 \times 10^{6}) \times (4.0 \times 10^{-3})}{4.2 \times 10^{-4}} \) and \( \frac{6.48 \times 10^{5}}{(2.4 \times 10^{4}) \times (1.8 \times 10^{-2})} \).Show Answer

19One tank holds \( 3.2 \times 10^{4} \) litres of water and a second tank holds \( 1.3 \times 10^{3} \) litres. How much water is there in the two tanks together?Show Answer

20A rocket has to travel \( 2.7 \times 10^{9} \) km and has already covered \( 1.35 \times 10^{9} \) km. How much of the journey is left?Show Answer

21How many equal tanks of \( 1.6 \times 10^{3} \) litres are needed to hold \( 9.6 \times 10^{6} \) litres of petrol?Show Answer

22A pond holds \( 1.8 \times 10^{8} \) litres of water. If \( 1.6 \times 10^{5} \) litres are let out, how much water is left? Give the answer in scientific notation.Show Answer

23Write \( 0.\overline{6} \) as a fraction and say whether it is rational.Show Answer

24A student wrote 0.000045 as \( 45 \times 10^{-6} \). Why is this not scientific notation? Give the correct answer.Show Answer

25The Earth is \( 1.496 \times 10^{8} \) km from the Sun and Mercury is \( 5.791 \times 10^{7} \) km from the Sun. How much farther from the Sun is the Earth?Show Answer

26Why is the Pythagoras theorem needed to show \( \sqrt{2} \) on the number line?Show Answer