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Mathematics

Decimal fractions

Educator section

Memorandum

13.4

a) 2 60 100 size 12{ { { size 8{"60"} } over { size 8{"100"} } } } {} 2,60
b) 13 625 1000 size 12{ { { size 8{"625"} } over { size 8{"1000"} } } } {} 13,625
c) 17 75 100 size 12{ { { size 8{"75"} } over { size 8{"100"} } } } {} 17,75
d) 23 875 1000 size 12{ { { size 8{"875"} } over { size 8{"1000"} } } } {} 23,875
e) 36 8 10 size 12{ { { size 8{8} } over { size 8{"10"} } } } {} 36,8

13.5 a) 0,83

  1. 0,2857142
  2. 0,8125
  3. 0,4

13.6

9 2 size 12{ { { size 8{9} } over { size 8{2} } } } {} 11 2 size 12{ { { size 8{"11"} } over { size 8{2} } } } {} 325 100 size 12{ { { size 8{"325"} } over { size 8{"100"} } } } {} 43 5 size 12{ { { size 8{"43"} } over { size 8{5} } } } {} 201 8 size 12{ { { size 8{"201"} } over { size 8{8} } } } {} 4056 1000 size 12{ { { size 8{"4056"} } over { size 8{"1000"} } } } {} 199 5 size 12{ { { size 8{"199"} } over { size 8{5} } } } {}
4 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} 5 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} 3 25 100 size 12{ { { size 8{"25"} } over { size 8{"100"} } } } {} 8 3 5 size 12{ { { size 8{3} } over { size 8{5} } } } {} 25 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} 4 56 1000 size 12{ { { size 8{"56"} } over { size 8{"1000"} } } } {} 39 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {}
4,5 5,5 3,25 8,6 25,125 4,056 39,8

14. a) 0,3

  1. 0,6
  2. 0,23

Leaner section

Content

Activity: more revision [lo 1.4.2, lo 1.10, lo 2.3.1, lo 2.3.3]

We can convert proper fractions to decimal fractions in this way:

13.2 Did you know?

We can also calculate it in this way:

13.3 Which of the methods shown above do you choose?

Why?

13.4 Complete the following tables:

13.5 Use the division method as shown in 13.2 and write the following fractions as decimal fractions:

a) 5 6 size 12{ { {5} over {6} } } {} ........................................................................... ...........................................................................

...........................................................................

b) 2 7 size 12{ { {2} over {7} } } {} ........................................................................... ...........................................................................

...........................................................................

c) 13 16 size 12{ { {"13"} over {"16"} } } {} ........................................................................... ...........................................................................

...........................................................................

d) 4 9 size 12{ { {4} over {9} } } {} ........................................................................... ...........................................................................

...........................................................................

13.6 Can you complete the following table??

Improper fraction 9 2 size 12{ { { size 8{9} } over { size 8{2} } } } {} 45 5 size 12{ { { size 8{"45"} } over { size 8{5} } } } {}
Mixed Number 5 1 2 size 12{5 { { size 8{1} } over { size 8{2} } } } {} 25 1 8 size 12{"25" { { size 8{1} } over { size 8{8} } } } {} 39 4 5 size 12{"39" { { size 8{4} } over { size 8{5} } } } {}
Decimal fraction 3,25 4,056

14. BRAIN-TEASERS!

Write the following fractions as decimal fractions. Try to do these sums first without a calculator!

a) 1 3 size 12{ { {1} over {3} } } {} ........................................................................... ...........................................................................

...........................................................................

b) 2 3 size 12{ { {2} over {3} } } {} ........................................................................... ...........................................................................

...........................................................................

c) 23 99 size 12{ { {"23"} over {"99"} } } {} ........................................................................... ...........................................................................

...........................................................................

15. Do you still remember?

We call 0,666666666 . . . a recurring decimal . We write it as 0, 6 size 12{0, {6} cSup { size 8{ cdot } } } {} .

0,454545 . . . is also a recurring decimal and we write it as 0, 4 5 size 12{0, {4} cSup { size 8{ cdot } } {5} cSup { size 8{ cdot } } } {} .

We normally round off these recurring decimals to the first or second decimal place, e.g.: 0, 6 size 12{0, {6} cSup { size 8{ cdot } } } {} becomes 0,7 or 0,67 and 0, 4 5 size 12{0, {4} cSup { size 8{ cdot } } {5} cSup { size 8{ cdot } } } {} becomes 0,5 or 0,45

16. Time for self-assessment

  • Tick the applicable block:
YES NO
I can:
Compare decimal fractions with each other and put them in the correct sequence.
Fill in the correct relationship signs.
Round off decimal fractions correctly to:
  • the nearest whole number
  • one decimal place
  • two decimal places
  • three decimal places
Convert fractions and improper fractions correctly to decimal fractions.
Explain what a recurring decimal is.

Assessment

Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.4: We know this when the learner recognises and uses equivalent forms of the rational numbers listed above, including:

1.4.2 decimals;

Assessment Standard 1.10: We know this when the learner uses a range of strategies to check solutions and judges the reasonableness of solutions.

Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.3: We know this when the learner represents and uses relationships between variables in a variety of ways using:

2.3.1 verbal descriptions;

2.3.3 tables.

Questions & Answers

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
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
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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
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Akash Reply
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Maciej
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Abigail
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Anassong
How can I make nanorobot?
Lily
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Mathematics grade 7. OpenStax CNX. Sep 16, 2009 Download for free at http://cnx.org/content/col11075/1.1
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