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1.1 Exercises

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       Theory          Exercises      


Exercise 1.1:1

Work out (without the help of a calculator)

a) 3−7−4+6−5 b) 3−(7−4)+(6−5)
c) 3−(7−(4+6)−5) d) 3−(7−(4+6))−5

Answer | Solution a | Solution b | Solution c | Solution d


Exercise 1.1:2

Simplify

a) (3−(7−4))(6−5) b) 3−(((7−4)+6)−5)
c) 3(−7)−4(6−5) d) 3(−7)−(4+6)(−5)

Answer | Solution a | Solution b | Solution c | Solution d


Exercise 1.1:3

Determine whether the following are natural numbers, integers, rational numbers or irrational numbers.

a) 8 b) −4 c) 8−4
d) 4−8 e) 8(−4) f) (−8)(−4)

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f


Exercise 1.1:4

Determine whether the following are natural numbers, integers, rational numbers or irrational numbers.{| width="100%" cellspacing="10px" |a) |width="33%"| 4−8 |b) |width="33%"| −4−8 |c) |width="33%"| \displaystyle \frac{\sqrt{2}}{3} |- |d) || \displaystyle \Bigl(\frac{4}{\sqrt{2}}\Bigr)^2 |e) || \displaystyle -\pi |f) || \displaystyle \pi+1 |}

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f


Exercise 1.1:5

Arrange the following numbers in ascending order

a) \displaystyle 2, \displaystyle \tfrac{3}{5}, \displaystyle \tfrac{5}{3} och \displaystyle \tfrac{7}{3}
b) \displaystyle -\tfrac{1}{2}, \displaystyle -\tfrac{1}{5}, \displaystyle -\tfrac{3}{10} och \displaystyle -\tfrac{1}{3}
c) \displaystyle \tfrac{1}{2}, \displaystyle \tfrac{2}{3}, \displaystyle \tfrac{3}{5}, \displaystyle \tfrac{5}{8} och \displaystyle \tfrac{21}{34}

Answer | Solution a | Solution b | Solution c


Exercise 1.1:6

Give the decimal expansion of the following to three decimal places.

a) \displaystyle \frac{7}{6} b) \displaystyle \frac{9}{4} c) \displaystyle \frac{2}{7} d) \displaystyle \sqrt{2}

Answer | Solution a | Solution b | Solution c | Solution d


Exercise 1.1:7

Which of the following numbers are rational? Express them as a fraction of two integers.

a) \displaystyle 3\textrm{.}14
b) \displaystyle 3\textrm{.}1416\,1416\,1416\,\ldots
c) \displaystyle 0\textrm{.}2\,001\,001\,001\,\ldots
d) \displaystyle 0\textrm{.}10\,100\,1000\,10000\,1\ldots\, (one 1:, one 0:, one 1:, two 0:s, one 1:, three 0:s etc.)

Answer | Solution a | Solution b | Solution c | Solution d

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