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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

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
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
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
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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Read about ancient clocks like_ hour glass, water clock and sun dial for a quiz and hand on Activity in the class
Neha Reply

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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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