Transition Year Maths PROJECT 1.2 Base 16


Write out the first 40 numbers in base 16, then add 216 to 1316 and multiply 216 × 1316. Check your answers – there are many conversion programmes available on the Internet.


Fractions can be confusing in bases other than 10. Consider the binary system: is 0·12


1 210


1 410


is 0·012


Base 10 has become the dominant system, most likely because we have 10 fingers on which to count. Societies with base 10 as their counting system have advanced faster scientifically, probably because it is easier to use. It is also speculated that the Roman Numeral system contributed to the fall of the Roman Empire, as place-value systems of base 5 from China and base 10 from the Middle East became more widely used.


PROJECT 1.3 Converting to Base 10


Consider the numbers 11111111112 22222222223 and 11111111113. Use the method from Example 4 to convert these numbers to base 10. Work in small groups to investigate if you can


find an easy or a short-cut way of doing any of these calculations. See the hint a the end of the chapter for the short-cut.


Questions NOTE


A subscript indicates the base. If no subscript is given, assume a base of 10.


1. Write the numbers from 10 to 30 in Roman Numerals.


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2. Write the dates from 1999 to 2012 in Roman Numerals.


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