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	NUMBER SYSTEMS
	Maths Workshop

2. LEARN HOW TO COUNT

2.1 Introduction

Imagine that you only have these five figures to count with: 0, 1, 2, 3 and 4.

You can see what would happen in the window below. Use the buttons to see. You would only be able to count up to 4444.

EXERCISE 1:

a) Which number comes next after 1244?

b) Which number comes next after 244044?

c) What about after 4444?

d) Which number comes just before 300300?

If we only use five figures to count with then we can call the number system we are working with base 5.

The most common number system has ten figures: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. It is called the decimal system or base 10.

2.2 Counting

In the window below we are going to use different number systems to count the blue dots that appear in the yellow rectangle.

Use the decimal number buttons to change the number of dots that appear in the yellow rectangle (you can only go up to 127) and use the base number buttons to choose the number system. Look carefully at how we use the different number systems to count with.

Use the window to complete the following exercise.

EXERCISE 2:

a) How do we express the decimal number 33 in base 5? What about in base 8?

If the base is greater than 10 we need to use some new symbols:

We shall use A to represent the decimal number 10, B to represent 11, and so on.

b) How do we express the decimal number 11 in base 11? What about in base 12?

c) Express the decimal number 43 in all bases between 2 and 16.

d) How do we express the number written as 5B in base 15, in the decimal system (base 10)?

e) How do we express the number written as 201 in base 3, in base 12?

f) In which base does 2+2=10?

You should have noticed that the same quantity is expressed differently depending on the base of its number system.

For example, to express the number 15 in base 7 we can write: 15₍₇

	Juan Simón Santamaría

	Spanish Ministry of Education. Year 2002

Except where otherwise noted, this work is licensed under a Creative Common License