Topicm9aa6513383b8ea63_1528449000663_0Topic

Exponential notation

Levelm9aa6513383b8ea63_1528449084556_0Level

Second

Core curriculumm9aa6513383b8ea63_1528449076687_0Core curriculum

I. Powers with rational bases. The student:

5) read and write number in the exponential notation a · 10Indeks górny k^k, when 1 ≤ a < 10, k is an integer number.

Timingm9aa6513383b8ea63_1528449068082_0Timing

45 minutes

General objectivem9aa6513383b8ea63_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm9aa6513383b8ea63_1528449552113_0Specific objectives

1. Writing numbers in the exponential notationexponential notationexponential notation.

2. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesm9aa6513383b8ea63_1528450430307_0Learning outcomes

The student:

- writes numbers in the exponential notation.

Methodsm9aa6513383b8ea63_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workm9aa6513383b8ea63_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm9aa6513383b8ea63_1528450127855_0Introduction

The teacher introduces the subject of the lesson – exponential notationexponential notationexponential notation. Such notation is used when we want to write down very small or very big numbers. In order to do that, we use powers with integer exponents.

Procedurem9aa6513383b8ea63_1528446435040_0Procedure

Students analyse the examples:

They notice that in changing a number into the product form, the second elements of the product is always smaller than 10. But the second elements has to be greater than what number? The teacher gives another examples:

0,1 = 1 ∙ 10Indeks górny -1^-1

0,0047 = 4,7 ∙ 10Indeks górny -3^-3

0,0000000587 = 5,87 ∙ 10Indeks górny -8^-8

Students notice that the second element is always a number greater or equal to 1.

Together they draw a conclusion:

Conclusion:

- A number written in the form of exponential notation has the form a · 10Indeks górny k^k, where $1 \le a < 10$ and k is an integer.m9aa6513383b8ea63_1527752256679_0- A number written in the form of exponential notation has the form a · 10Indeks górny k^k, where $1 \le a < 10$ and k is an integer.

Students use obtained knowledge in the exercises.

Task
Students work individually, using computers. Their task is to present the numbers in the exponential notationexponential notationexponential notation.

[Geogebra applet]

Then they used shaped abilities in the exercises.

Task
Write the number in the exponential notation.

a) 0,0027

b) 2,7

c) 0,027

d) 2700

e) 0,00027

Task
Calculate how much more dmIndeks górny 3³ of water will fit into a 350 ml bottle whose capacity
2 ∙ 10Indeks górny -1^-1 dmIndeks górny 3³. Give the result in the exponential notation.m9aa6513383b8ea63_1527752263647_0Calculate how much more dmIndeks górny 3³ of water will fit into a 350 ml bottle whose capacity
2 ∙ 10Indeks górny -1^-1 dmIndeks górny 3³. Give the result in the exponential notation.

Task
Fill the dotted spaces with the exponent of the powerexponent of the powerexponent of the power.

a) 4,7 ∙ 10Indeks górny nⁿ = 47000   n = …

b) 3,42 ∙ 10Indeks górny nⁿ = 3420000   n = …

c) 3,9 ∙ 10Indeks górny nⁿ = 390   n = …

d) 1,5 ∙ 10Indeks górny nⁿ = 0,015   n = …

e) 7,81 ∙ 10Indeks górny nⁿ = 0,0000781   n = …

Task 
Fill in the dotted spaces using the exponential notationexponential notationexponential notation.

a) 35 cm = … m

b) 2 mm = … cm

c) 0,36 m = … km

d) 0,3 g = … dag

e) 0,05 kg = … t

Task 
Insert a proper sign in the dotted space: <, >, =.

a) 9 ∙ 10Indeks górny 3³ … 6 ∙ 10Indeks górny 4⁴

b) 0,4 ∙ 10Indeks górny 6⁶ … 3,5 ∙ 10Indeks górny 5⁵

c) 49 ∙ 10Indeks górny 4⁴ … 0,49 ∙ 10Indeks górny 6⁶

d) 1,7 ∙ 10Indeks górny -4^-4 … 4,8 ∙ 10Indeks górny -3^-3

e) 24 ∙ 10Indeks górny -5^-5 … 0,75 ∙ 10Indeks górny -6^-6

An extra task:
How many times the Surface of Earth is greater than the Surface of the Moon? Write the result in the exponential notationexponential notationexponential notation. Look for the necessary data in available data sources.

The teacher sums up the lesson by saying that the exponential notation, also called scientific or engineering notation, allows us to write down very big or very small numbers.

Lesson summarym9aa6513383b8ea63_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

- A number written in the form of exponential notation has the form
a · 10Indeks górny k^k, where $1 \le a < 10$ and k is an integer.

Selected words and expressions used in the lesson plan

Avogadro numberAvogadro numberAvogadro number

base of the powerbase of the powerbase of the power

comparing numberscomparing numberscomparing numbers

exponent of the powerexponent of the powerexponent of the power

exponential notationexponential notationexponential notation