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With a calculator:

2. Make decimal fractions from the following:

2.1 3 4 size 12{ { {3} over {4} } } {} = 3  4 = 0, ____

2.2 2 5 size 12{ { {2} over {5} } } {} = 25 =
2.3 3 5 size 12{ { {3} over {5} } } {} =
2.4 4 5 size 12{ { {4} over {5} } } {} =
2.5 5 5 size 12{ { {5} over {5} } } {} =
2.6 1 4 size 12{ { {1} over {4} } } {} =

We can convert any ordinary fraction to decimals in that way.

3. Make one-third into a decimal: 1 3 size 12{ { {1} over {3} } } {} = 1  3 =_____

Can you think of a reason why the answer is the way it is?

Without a calculator:

4. Write down equivalent fractions for each of the following and then write them as decimal fractions:

Fraction Fraction as tenths Decimal fraction
half
one third Can’t
Fraction Fraction as tenths Decimal fraction
two-thirds Can’t
one-quarter
three-quarters
one-fifth
two-fifths
three-fifths
four-fifths
one-sixth Can’t
one-eighth

(Some of the above have more than one decimal place but it is good to know about them.)

5. What about the thirds and sixths and others that cannot be made into tenths? Use division.

  • one-third = 1  3 =
  • two-thirds = 2  3 =

Use your own method for the division or use a calculator. 1 3 size 12{ { {1} over {3} } } {} = 1  3

Or one way: ? x 3 = 1

0 x 3 = 0,0

0,3 x3 = 0,9

0,03 x 3 = 0,09

0,99 (which is nearly 1)

so: (0 x 3) + ( 0,3 x 3) + ( 0,03 x 3)

0 + 0,3 + 0,03

= 0,333

(and the calculator will go on dividing: 0,333)

We say: 0,3 recurring or 0,3֯(The dot means recurring.)

TEST YOUR PROGRESS

1. Solve without a calculator:

1.1 17 × 26

1.2 153  9

2. Share 11 sausage rolls equally amongst 10 boys. How much sausage roll will each boy receive?

3. Share 12 sausage rolls equally amongst 10 boys. How much sausage roll will each boy receive?

4. Mike drinks 1 1 2 size 12{ size 11{1 { {1} over {2} } }} {} mugs of milk for breakfast. His sister, Sharon, drinks 3 4 size 12{ { {3} over {4} } } {} of a mug of milk. How much milk have they drunk altogether?

5. Write the following in expanded notation:

5.1 64,8 =
5.2 341,2 =

6. Write as decimals:

  • Three and four-fifths = ………………………
  • One and three-tenths = ………………….
  • Five and one-quarter = …………………
  • 4 1 2 size 12{ size 11{4 { {1} over {2} } }} {} = ………………….

7. From<;>; = write down the correct sign to make the following true:

  • 2,4 ____ 4,2
  • 1,7 _____2,1

8. Write down the number that is:

Answer
one tenth more than 45,9
one tenth less than 10

Assessement

Learning outcomes(LOs)
LO 1
Numbers, Operations and RelationshipsThe 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 standards(ASs)
We know this when the learner:
1.1 counts forwards and backwards in a variety of intervals;
1.3 recognises and represents the following numbers in order to describe and compare them: common fractions with different denominators, common fractions in diagrammatic form, decimal fractions and multiples of single-digit numbers;
1.3.2 common fractions with different denominators, including halves, thirds, quarters, fifths, sixths, sevenths and eighths;
1.3.3 common fractions in diagrammatic form;
1.3.4 decimal fractions of the form 0,5; 1,5 and 2,5; etc., in the context of measurement;
1.3.6 multiples of single-digit numbers to at least 100;
1.5 recognises and uses equivalent forms of the numbers including common fractions and decimal fractions;
1.5.1 common fractions with denominators that are multiples of each other;
1.5.2 decimal fractions of the form 0,5; 1,5 and 2,5, etc., in the context of measurement;
1.7 solves problems that involve comparing two quantities of different kinds (rate);
1.7.1 comparing two or more quantities of the same kind (ratio);
1.8 estimates and calculates by selecting and using operations appropriate to solving problems that involve addition of common fractions, multiplication of at least whole 2-digit by 2-digit numbers, division of at least whole 3-digit by 1-digit numbers and equal sharing with remainders;
1.8.3 addition of common fractions in context;
1.8.6 equal sharing with remainders;
1.9 performs mental calculations involving:
1.9.2 multiplication of whole numbers to at least 10 x 10;
1.12 recognises, describes and uses:, and
1.12.1 the reciprocal relationship between multiplication and division (e.g. if 5 x 3 = 15 then 15 ÷ 3 = 5 and 15 ÷ 5 = 3;
1.12.2 the equivalence of division and fractions (e.g. 1 ÷ 8 = ⅛);
1.12.3 the commutative, associative and distributive properties with whole numbers.
Learning outcomes(LOs)
LO 2
Patterns, Functions and AlgebraThe learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.
Assessment standards(ASs)
We know this when the learner:
2.1 investigates and extends numeric and geometric patterns looking for a relationship or rules;
2.1.1 represented in physical or diagrammatic form;
2.1.2 not limited to sequences involving constant difference or ratio;
2.1.3 found in natural and cultural contexts;
2.1.4 of the learner’s own creation;
2.2 describes observed relationships or rules in own words;
2.3 determines output values for given input values using verbal descriptions and flow diagrams;
2.3.1 verbal descriptions;
2.3.2 flow diagrams.

Memorandum

ACTIVITY 1: recognising and representing decimal fractions

1.1 Missing numbers: 10; 1; one-tenth

1.2 Calculator answers: 10; 1; 0,1

0,1 means one-tenth

2.1

x 1 000 x 100 x 10 x 1 x 0,1
(a) 1 4 5 6 3
(b) 4 6 0 1 9
(c) 8 5
(d) 3 1 7
(e) 4 5 6 2

2.2 (b) 4 x 1 000 + 6 x 100 + 0 x 10 + 1 x 1 + 9 x 0,1

(c) 0 x 1 000 + 0 x 100 + 0 x 10 + 8 x 1 + 5 x 0,1 or just: 8 x 1 + 5 x 0,1

(d) 0 x 1 000 + 0 x 100 + 3 x 10 + 1 x 1 + 7 x 0,1 or just: 3 x 10 + 1 x 1 + 7 x 0,1

(e) 0 x 1 000 + 4 x 100 + 5 x 10 + 6 x 1 + 2 x 0,1 or just: 4 x 100 + 5 x 10 + 6 x 1 + 2 x 0,1

ACTIVITY 2: comparing decimal fractions

1.1<

1.2 

1.3<

1.4<

1.5 

1.6<

2. Encircled number: 49,1

3.1 10,9

3.2 5,4

3.3 5,9

3.4 8,2

3.5 7

3.6 99,1

3.7 5,9

3.8 9,9

ACTIVITY 3: converting from fractions to decimal fractions and vice versa

1. Discussion

2. With a calculator

  • 0,75
  • 2.2 0,4
  • 2.3 0,6
  • 2.4 0,8

2.5 0,8

2.6 0,25

3. 0,33333

4.

Fraction Fraction as tenths Decimal fraction
half Five tenths 0,5
One-third Can’t 0,3333
Two-thirds Can’t 0,6666
One-quarter Can’t; 0,25
Three-quarters Can’t; 0,75
One-fifth Two-tenths 0,2
Two-fifths Four-tenths 0,4
Three-fifths Six-tenths 0,6
Four-fifths Eight-tenths 0,8
One-sixth Can’t 0,1666
One-eighth Can’t; 0,125
  • 0,333
  • 0,666

Test your progress

1.1 442

1.2 17

2. one and one-tenth or 1,1 sausage rolls

3. one and two-tenths or 1 and a fifth sausage rolls (or 1,2)

4. two and a quarter mugs

  • 6 x 10 + 4 x 1 + 8 x 0,1
  • 3 x 100 + 4 x 10 + 1 x 1 + 2 x 0,1
  • 3,8
  • 1,3
  • 5,25
  • 4,5
  • <
  • <
  • 46
  • 9,9

Questions & Answers

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
it is a goid question and i want to know the answer as well
Maciej
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Abigail
Do somebody tell me a best nano engineering book for beginners?
s. Reply
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
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
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s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
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Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
what is the function of carbon nanotubes?
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I'm interested in nanotube
Uday
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Ramkumar Reply
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what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
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what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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anybody can imagine what will be happen after 100 years from now in nano tech world
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after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
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Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
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Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Mathematics grade 4. OpenStax CNX. Sep 18, 2009 Download for free at http://cnx.org/content/col11101/1.1
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