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1.1 Exercises

From Förberedande kurs i matematik 1

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===Övning 1.1:1===
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===Exercise 1.1:1===
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Work out (without the help of a calculator)
Work out (without the help of a calculator)
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===Övning 1.1:2===
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===Exercise 1.1:2===
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Simplify
Simplify
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===Övning 1.1:3===
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===Exercise 1.1:3===
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Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
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===Övning 1.1:4===
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===Exercise 1.1:4===
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Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?
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===Övning 1.1:5===
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===Exercise 1.1:5===
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Arrange the following numbers in ascending order
Arrange the following numbers in ascending order
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===Övning 1.1:6===
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===Exercise 1.1:6===
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Give the decimal expansion of the following to three decimal places.
Give the decimal expansion of the following to three decimal places.
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===Övning 1.1:7===
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===Exercise 1.1:7===
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Which of the following numbers are rational? Give them as a fraction of two integers.
Which of the following numbers are rational? Give them as a fraction of two integers.

Revision as of 11:04, 3 August 2008

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Exercise 1.1:1

Work out (without the help of a calculator)

a) 374+65 b) 3(74)+(65)
c) 3(7(4+6)5) d) 3(7(4+6))5


Exercise 1.1:2

Simplify

a) (3(74))(65) b) 3(((74)+6)5)
c) 3(7)4(65) d) 3(7)(4+6)(5)


Exercise 1.1:3

Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?

a) 8 b) 4 c) 84
d) 48 e) 8(4) f) (8)(4)


Exercise 1.1:4

Which of the following belong to the natural numbers? integers? rational numbers? irrational numbers?

a) 48 b) 48 c) 32 
d) 422  e) f) +1


Exercise 1.1:5

Arrange the following numbers in ascending order

a) 2, 53, 35 och 37
b) 21, 51, 310 och 31
c) 21, 32, 53, 85 och \displaystyle \tfrac{21}{34}


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}


Exercise 1.1:7

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

a) \displaystyle 3{,}14
b) \displaystyle 3{,}1416\,1416\,1416\,\ldots
c) \displaystyle 0{,}2\,001\,001\,001\,\ldots
d) \displaystyle 0{,}10\,100\,1000\,10000\,1\ldots\, (en 1:a, en 0:a, en 1:a, två 0:or, en 1:a, tre 0:or osv.)