Unit 3NumbersIntroductionThis unit is all about numbers. You use numbers in many different waysevery day; for example, you might use them to tell the time, look for aparticular page in a book, find the price of an item that you want to buy,check your bank balance or make a measurement. You probably don’tthink about the numbers themselves, and the interesting properties thatthey have, but these properties have fascinated many people for thousands‘Why are numbers beautiful?It’s like asking why isBeethoven’s Ninth Symphonybeautiful. If you don’t seewhy, someone can’t tell you.I know numbers are beautiful.If they aren’t beautiful,nothing is.’Paul Erd¨os (1913–1996),Hungarian mathematician.Paul Erd¨os was one of themost unusual and prolificmathematicians in history.He travelled constantly, livingout of a suitcase, andcollaborated with othermathematicians wherever hewent.of years. This unit will give you just a glimpse of the many properties ofnumbers.In particular, you will learn about some properties of prime numbers, andabout different types of numbers, such as rational and irrational numbers,and how they differ from each other.Numbers are of course an important part of mathematics, and it isessential that you are able to work with them confidently and performcalculations with them, both by hand and by using your calculator. Theseskills will underpin much of your later work in the module, so this unit alsogives you an opportunity to revise and practise some of your skills inworking with numbers, and to learn some new number skills. If you are alittle rusty on some of the basic number skills, such as adding fractions,then you may find that you need more detail than is provided in this unit.If so, then you should find it helpful to consult Maths Help via the link onthe module website.In the final section of the unit, you will look at how numbers in thecontext ofratioare useful in all sorts of everyday situations. In particular,you will learn aboutaspect ratio, which provides a way to describe theshapes of rectangles. Many forms of media involve rectangular shapes; forexample, computer and television screens, photographs, printed pages andvideo pictures are all usually rectangular. Aspect ratio is important indetermining, for example, how well different shapes of rectangular picturefit on different shapes of rectangular screen.The calculator section of the MU123 Guide is needed for two of theactivities in this unit. If you do not have the MU123 Guide to hand whenActivities 27 and 35, onpages 148 and 159, respectively,are in the MU123 Guide.you reach these activities, then you can omit them and return to themlater.1 Natural numbersAs you saw in Unit 1, theintegersare the numbers. . . ,−3,−2,−1,0,1,2,3,. . . .This section is about thepositive integers,1,2,3, . . . ,which are also known as thenatural numbers.