3.2.1 Try some yourself 1 Convert each of the following to percentages. Round off the percentages to whole numbers. (a) (i) 0.8 (ii) 0.21 (iii) 0.70< 3.2 Converting to a percentage Fractions and decimals can also be converted to percentages, by multiplying by 100%. So, for example, 0.17, 0.3 and 0.17 × 100% = 17%; 0.3 × 100% = 30%; Author(s): 3.1.1 Try some yourself 1 Express each of the following percentages as fractions: (a) 40% (b) 8% (c) 70% (d) 3.1 What are percentages? Percentages are used, particularly in newspaper articles, to indicate fractions (as in ‘64% of the population voted’) or to indicate changes (as in ‘an increase of 4%’). Percentages often indicate proportions. For example, labels in clothes indicate the various proportions of different yarns in the fabric. ‘Per cent’ means ‘per hundred’ and is denoted by the symbol %. 100% is the same as the whole, or one hundred per hundred. 2.3 Inverse proportion In Section 2.2 you saw that direct proportion described relationships between two quantities, where as one increased, so did the other. Sometimes as one quantity increases the other decreases instead of increasing. This is called indirect proportion. Team tasks are often an example of this. The time taken to do a job is indirectly proporti 2.2.1 Try some yourself 1 A recipe for four people calls for 2.2 Direct proportion In a recipe the quantity of each ingredient needed depends upon the number of portions. As the number of portions increases, the quantity required increases. The quantity per portion is the same. This is called direct proportion. The quantity is said to be directly proportional to the number of portions. If 2 potatoes are required for one portion, 4 will be required for two portions etc. A useful method for direct proportion problems is to find the quantity for one and multiply by the 2.1 Introduction Proportion is another way of expressing notions of part and whole. You might say that the proportion of village inhabitants who are children is a quarter, or that the proportion of fruit juice in the punch is two thirds, or that the proportion of sand in the concrete is three quarters. All these examples involve the fractions Introduction This unit is from our archive and it is an adapted extract from Open mathematics (MU120) which is no longer in presentation. If you wish to study formally at The Open University, you may wish to explore the courses we offer in this curriculum area
The topics in this unit, ratios, proportion and percentages, are concerned with dividing something into parts. Fo 4.3 Further exercises Let Examples 1. The relation ‘is equal to’ on It is reflexive since, for all x Relations We shall use the symbol Some texts use ρ, rather than 1.1 Rational numbers In OpenLearn unit M208_5 Mathematical language you met the sets Learning outcomes After studying this unit you should be able to: understand the arithmetical properties of the rational and real numbers; understand the definition of a complex number; perform arithmetical operations with complex numbers; represent complex numbers as points in the complex plane; determine the polar form of a complex number; use de Moivre's Theorem to find the nth roots o Introduction In this unit we look at some different systems of numbers, and the rules for combining numbers in these systems. For each system we consider the question of which elements have additive and/or multiplicative inverses in the system. We look at solving certain equations in the system, such as linear, quadratic and other polynomial equations. In Section 1 we start by revising the notation used for the rational numbers and the real numbers, and we list their arithmetical prop Acknowledgements Except for third party materials and otherwise stated (see terms and conditions). This content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence 1. Join the 200,000 students currently studying with The Open Unive 5.3.3 Torus with 1 hole In our last example, we consider a pentagon with two pairs of edges identified. As we saw in Section 2.3, identification of the edges produces a torus with a hole. In this case there are five vertex-neighbourhoods to fit together, as shown in Author(s): 5.3.2 Klein bottle If x lies on an edge, then each of the two points in [x] has a half-disc-like neighbourhood (see Figure 107). When we identify edges, these neighbourhoods fit together to form disc-like neighbourhoods in the Klein bottle. 5.3.1 Torus If x lies on an edge, then each of the two points in [x] has a half-disc-like neighbourhood. When we identify edges, these neighbourhoods fit together to form disc-like neighbourhoods on the torus, as Figure 105 shows. 5.3 Neighbourhoods We know that a polygon X is a surface and so each point x in X has a disc-like or half-disc-like neighbourhood. We shall show that a map f that identifies edges of a polygon to create an object Y automatically creates corresponding disc-like or half-disc-like neighbourhoods of each point y = f(x) of Y. If x is in the interior of X, there is no difficulty: the point x has a disc-like neighbourhood U
can be expressed as percentages as follows:
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Exercise 59
is reflexive, symmetric and transitive.
(known as tilde or twiddle) to represent a relation between two elements of a set.Author(s):
= {1, 2, 3, …}, the natural numbers;
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