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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

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
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
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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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