chapter 1 number. number systems – introduction of zero
TRANSCRIPT
Chapter 1
Number
Number systems – introduction of zero
Who invented 0?
Historical timeline of the development of numbers
Put these events in order – around what date did each occur?
First identified use of decimal (base 10) system
First recognised use of fractions
Definition of multiplication
Creation of times tables
Formulas for area and volume of solids
Evidence that every non-prime number can be written as a unique product of primes Introduction of
symbols to represent unknown numbers
First reference to irrational numbers
First evidence of zero
Decimal fractions (tenths, hundredths, etc.)
Symbolic system of algebra
Decimal system using the decimal point
Introduction of calculus
First use of πIdentified that π was roughly 3
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What if we didn’t have numbers?
What would happen if we didn’t have numbers?
Prepare a one-minute presentation to the class about why numbers are necessary.
TOK
Structure of numbers
Is Mathematics like English?Sentences are made up of different types of words.
Whole numbers are the natural numbers including zero. Not all whole numbers are natural numbers, but all natural numbers are whole numbers.
Wholewhole
wholenatural
natural
natural
Nouns provide the objects of the sentence, like bullet points. Without them there is no structure. Are they like whole numbers?
Adjectives are ‘describing’ words.They make sense of the nouns and provide context for them.Could they be like fractions and decimals?
Are numbers structured like sentences?
numbers
numbersnumbers
numbersnumbersnumbers.
zero
TOK
Classification of numbers
Sort these numbers in a sensible way
All of these numbers are Real Numbers
The rest of the numbers are called
Irrational Numbers
Numbers that make fractions are
called Rational Numbers
Sort these numbers in a sensible way
All of these numbers are Real Numbers
The rest of the numbers are called
Irrational Numbers
Numbers that make fractions are
called Rational Numbers
If a number is whole then it is an
Integer
Sort these numbers in a sensible way
All of these numbers are Real Numbers
The rest of the numbers are called
Irrational Numbers
Numbers that make fractions are
called Rational Numbers
If a number is whole then it is an
Integer
Natural Numbers
The effect of error
Currency rates
1 GDP = 1.1573 EUR1 USD = 1.4753 EUR
You are buying a house in Italy for €250,000.
You need to convert your currency into euros and see the exchange rates given above.
Your bank rounds the exchange rates to two decimal places.
Does this matter?
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The scale of numbers
