UNIT 4 Scientific Notation: Teaching Notes
MEP Jamaica: STRAND A
UNIT 4 Scientific Notation
Teaching Notes
Introduction
Scientific notation, or standard form, as it is often referred to, is a very convenient way of writing both
very large and very small numbers. It was not created, as such, but developed from the use of indices
in the form 10 n (n positive integer). For example, you can write
30 000 = 3 × 10 4
This is not much of a gain, but consider
1 000 000 000 = 1 × 10 9
and
0.0000001 = 1 × 10 − 7
where the scientific notation is much more concise that the alternative form.
Another example of the efficiency of this notation becomes obvious writing down the mass of the
Earth, which is
5933600 000 000 000 000 000 000 kg = 5.9336 × 10 24 kg
Teaching Points
Introduction
This 'modern' notation appears to have been first used by the French mathematician, René Descartes
(1596 - 1650) in 1637. Its widespread use in the 18th and 19th centuries was probably due to the need
for very accurate measurements. More recently, the development of calculators and computers has
further increased its use as it is a very convenient and efficient way of storing large and small
numbers. Scientific notation is also referred to as exponential notation by the designers of calculators:
they use the letter E to refer to the 'exponent' n, when writing any numbers in the form
a × 10 n
when 1 ≤ a < 10 and n (the exponent) is an integer.
This is a unique way of writing any number but note the restrictions on the number a are needed to
make it unique. For example, you could write
360 = 360 × 10 0
= 36 × 10 1
= 3.6 × 10 2
= 0.36 × 10 3 , etc.
but only 3.6 × 10 2 conforms to the rule 1 ≤ a < 10 and this is the unique way of writing 360 in
standard form.
This concept of uniqueness should be stressed when teaching this topic as well as the fact that any
number can be written in this form, to whatever degree of accuracy is required. For example,
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4 632 713
= 4.632713 × 10 6
0.003927
= 3.927 × 10 − 3
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MEP Jamaica: STRAND A
UNIT 4 Scientific Notation: Teaching Notes
UNIT 4 Scientific Notation
Teaching Notes
Language / Notation
• Standard form, scientific notation and exponential notation
Key Points
• Any number can be written in standard form as
a × 10 n
when 1 ≤ a < 10 and n is an integer.
• The restrictions on the number a, that is 1 ≤ a < 10 , are needed to ensure the uniqueness
of standard form.
Misconceptions
•
10 0 = 0 (rather than 1)
•
10 −1 = − 10 (rather than
1
)
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• 10 a × 10 b = 10 a × b (rather than 10 a + b )
• 10 a ÷ 10 b = 10 a ÷ b (rather than 10 a − b )
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