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 – Express large and small numbers in scientific notation.
 – Use your GDC (Graphic Display Calculator) to find numbers in scientific notation.
Consider the number:
123.4567
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There are two ways to round up the number by using fewer digits:
1. In a specific number of decimal places (d.p.)
in 1 d.p. 123.5
in 2 d.p. 123.46
in 3 d.p. 123.457
2. In a specific number of significant figures (s.f.). For the position of cutting we start counting from the first nonzero digit:
in 4 s.f. 123.5in 5 s.f. 123.46
InchangĆ© : in 6 s.f. 123.457
But also
in 2 s.f. 120
InchangĆ© : in 1 s.f. 100
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Important remark: In the final IB exams the requirement is to giveInchangĆ© : the answers either in exact form or in 3 s.f.
For example:
\(2\pi\)6.28
Exact form  in 3 s.f. 
\(\sqrt{2}\)  1.41 
12348  12300 
METHOD:
The method is the same as with decimal places except that you start counting from theInchangĆ© : very beginning of the number (instead of just after the decimal point):
– If 5 or above then round the last number up.
– If 4 or below the last number stays the same
Examples:
a. Round 15.748 to 3 significant figures.
b. Round 64.3463 to 2 significant figures.
c. Round 128.35 to 2 significant figures.
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Exercise
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Find each of these values as a power of 10.
Example : 1 000 = 10^{3 }
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Ā Find each of these values as a power of 10.
Example : 0.001 = 10^{3 }
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Reminder
For a positive integer n :
 \(10^{\color{red}{n}}\) is written with a 1 followed by n zeros.
 \(10^{\color{green}{n}}\) is written with a 1 preceded by n zeros.
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Exercise :
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answer the question writing the letter, like this : \(s=2\)
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How can we use our findings so far to express numbers as multiple of powers of ten .
For example \( 8, 000\) :
\( 8, 000 = 8 \times 1,\color{green}{000} \) and we know\( 1, \color{green}{000} = 10^{\color{green}{3}}\)
so, \( 8, \color{green}{000} = 8\times10^{\color{green}{3}}\)
what about \( 60 ,000 ,000 \) ?
\( 6\color{green}{0, 000 ,000 }= 6\times 1\color{green}{0 ,000 ,000}\)
\( 6\color{green}{0, 000, 000}= 6\times 10^{\color{green}{7}}\)
and \( 0.005 \)?
\(\color{red}{ 0.00}5=5\times \color{red}{ 0.00}1\)
\(\color{red}{ 0.00}5=5\times 10^{\color{red}{ 3}}\)
Match all these numbers with their form in \(a\times 10^{k}\) where \( k \in \mathbb{Z}\)
Exercise
Scientific Notation
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Any number can written in the form :
\( a \times 10^k\) where \( 1 \leq a<10 \) and \( k\in \mathbb{Z}\)
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Scientific notation is a standard way of writing very large and very small numbers so that theyāre easier to both compare and use in computations.
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Examples :
METHOD:
ĀWrite 427 000 000 000 in scientific notation:

Write 0.00 000 037 in scientific notation.

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Exercise ā Level š
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Exercise ā Level š š
Exercise ā Level š š š
Exercise ā Level š š š š
Most calculators use the symbol EĀ± for the scientific notation:
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1.325E79 means \(1.325\times 10^{79}\) 
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Exercise :
NOTICE :
They may ask us to give the number in scientific form but also in 3 s.f. Then :
\(1.2345Ć10^{2}ā 1.23Ć10^{2}\)
\(3.2045Ć10^{5}ā 3.20Ć10^{5}\)
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Quizizz as a warm up or at the end of your course. This resource can be used by the students themselves by clicking on the “practice” button:
– Significant figures– Powers of 10– Scientific notation– Scientific notationcalculation 