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Mathematics

Grade 8

Rational numbers, circles and triangles

Module 15

Differentiating between rational and irrational numbers

Activity 1

Differentiating between rational and irrational numbers

[lo 1.2.7]

1. Can you remember what each of the following represents?

N = { ........................................................................... }

N 0 = { ........................................................................... }

Z = { ........................................................................... }

R = { ........................................................................... }

2. Provide the definition for:

a rational number:

an irrational number:

3. How would you represent each of the following?

3.1 Rational number......................... 3.2 Irrational number .........................

4. Complete the following table by marking relevant numbers with an X:

5. Select the required numbers from the list:

2 3 size 12{ { { size 8{ - 2} } over { size 8{3} } } } {} ; 1 + 4 size 12{ sqrt {4} } {} ; 9 + 4 size 12{ sqrt {9+4} } {} ; -4 ; 12 1 5 size 12{"12" { { size 8{1} } over { size 8{5} } } } {} ; 1 + 2 2 size 12{ { {1+ sqrt {2} } over { sqrt {2} } } } {}

5.1 Integers:

5.2 Rational numbers:

5.3 Irrational numbers:

6. Explain what you know about an equivalent fraction.

7. Provide two equivalent fractions for the following: 2 7 size 12{ { { size 8{2} } over { size 8{7} } } } {} = ............... = ...............

8. Provide the terms used to identify each of the following (e.g. proper fraction):

8.1 2 7 size 12{ { { size 8{2} } over { size 8{7} } } } {}

8.2 7 2 size 12{ { { size 8{7} } over { size 8{2} } } } {}

8.3 6 2 7 size 12{6 { { size 8{2} } over { size 8{7} } } } {}

8.4 0,67

8.5 0, 6 ˙ 7 ˙ size 12{0, { dot {6}} { dot {7}}} {}

8.6 23 %

Any of the above can be reduced to any of the others.

Activity 2:

Reduction of fractions to decimal numbers / recurring decimal numbers and vice versa

[lo 1.2.2, 1.2.6, 1.3, 1.6.1, 1.9.1]

  1. Use your pocket calculator to reduce the following fraction to a decimal number:

2. Explain how you would reduce this to a decimal number without the use of your pocket calculator. There are two methods:

Method 1: .................................................. (reduce denominator to 10 / 100 / 1 000)

Method 2: .................................................. (do division)

(Let your educator assist you.)

  • Do you see that the answer is the same – if the denominator cannot be reduced to multiples of 10 you have to apply the second method.

3. Now reduce each of the following to decimal numbers (round off, if necessary, to two digits):

3.1 5 8 size 12{ { { size 8{5} } over { size 8{8} } } } {} ..................................................

3.2 13 4 size 12{ { { size 8{"13"} } over { size 8{4} } } } {} ..................................................

3.3 5 3 4 size 12{5 { { size 8{3} } over { size 8{4} } } } {} ..................................................

3.4 3 7 8 size 12{3 { { size 8{7} } over { size 8{8} } } } {} ..................................................

3.5 6 7 size 12{ { { size 8{6} } over { size 8{7} } } } {} ..................................................

3.6 7 9 size 12{ { { size 8{7} } over { size 8{9} } } } {} ..................................................

4. Write the following decimal numbers as fractions or mixed numbers:(N.B.: All fractions have to be presented in their simplest form.)

4.1 6,008 ..................................................

4.2 4,65 ..................................................

4.3 0,375 ..................................................

4.4 7,075 ..................................................

4.5 13,65 ..................................................

4.6 0,125 ..................................................

5. How do we reduce fractions to recurring decimal numbers?

E.g. 5 11 size 12{ { { size 8{5} } over { size 8{"11"} } } } {}

Step 1: place a comma after the 5, i.e. 5, 0000

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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Source:  OpenStax, Mathematics grade 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
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