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Mathematics

Grade 4

Numbers, feactions, decimals and number patterns

Module 9

Recognise and represent fractions

Activity 1:

To recognise and represent decimal fractions [LO 1.3]

RECOGNIZING DECIMALS

1. What are decimals?

1.2 Think back to Place Value: Thousands; Hundreds; Tens and Units.

Complete the following:

1 000  10 = 100
100  10 =
10  10 =
110 = ?

1.3 Now check your answers on the calculator.

The calculator says that 1 10 = 0,1. What does 0,1 then mean? Discuss with a friend.

1.4 Draw lines on the bar below to show tenths. One has been divided by 10. We say that 0,1 is one tenth. It is the only way in which calculators can write one tenth, because of the way that they have been programmed. Now label each section on the bar below 0,1.

What is the meaning of 0,1? We have found that 1  10 = 0,1.

Think back to Fractions: we said: 1  2 = 1 2 size 12{ { {1} over {2} } } {}

So 1  10 = 1 10 size 12{ { {1} over {"10"} } } {}

1  10 = 1 10 size 12{ { {1} over {"10"} } } {} = 0,1

0,1 is just another way of writing 1 10 size 12{ { {1} over {"10"} } } {}

Study the diagram:

Thousands1 000 Hundreds100 Tens10 Units1 Tenths
Thousands1 000 Hundreds100 Tens10 Units1 Tenths 1 10 size 12{ { {1} over {"10"} } } {}
7 1 9 3 6
5 0 6 9 1

How do we show the end of the whole number when there are no headings?

We use a DECIMAL COMMA.

What are the numbers that have been written in the columns?

  • 7 193, 6 = 7 × 1 000 + 1 × 100 + 9 × 10 + 3 × 1 + six tenths
  • 5 069,1 = 5 × 1 000 + 0 + 6 × 10 + 9 × 1 + 1 10 size 12{ { {1} over {"10"} } } {}

Our calculators cannot write common fractions as we can; they are only machines that have been programmed to use place value, so they can only write decimal fractions.

Remember: We use a DECIMAL COMMA

to show the END OF THE WHOLE NUMBER

and the BEGINNING OF THE DECIMAL FRACTION

2. Now write the following decimal numbers in their expanded form under the correct heading in the columns below:

2.1 (a) 1 456,3 (b) 4 601,9 (c) 8,5 (d) 31, 7 (e) 456,2

X 1 000 × 100 × 10 × 1 × 0,1(tenths)
(a)
(b)
(c)
(d)
(e)

The FIRST digit after the decimal comma is always TENTHS.

2.2 Now write them again in their expanded form:

(a) 1 456,3 = 1 × 1 000 + 4 × 100 + 5 × 10 + 6 × 1 + 3 × 0,1

Activity 2:

To compare fractions [LO 1.5]

1. Carefully consider the value of each digit and use the correct sign from:<;  ; = to>compare the following:

1.1 1,5 _____1,7 1.4 45,9 ____62,3

1.2 6,3 ____ 6,1 1.5 13,2 ____8,6

1.3 24,7____ 42,3 1.6 57,5 ____58,2

2. Encircle the largest number:

43,7; 41,9; 43,1; 49,1; 41,5

3. Write down the number that is:

Answer Answer
3.1 one more than 9,9 3.1 3.5 0,1 less than 7,1 3.5
3.2 0,1 more than 5,3 3.2 3.6 0,1 more than 99,0 3.6
3.3 0,1 less than 6 3.3 3.7 0,1 more than 5,8 3.7
3.4 0,1 less than 8,3 3.4 3.8 0,1 less than 10 3.8

Activity 3:

To convert from fractions to decimal fractions and vice versa [LO 1.5]

Group discussion.

1. Read the following conversation between John and Sarah.

  • Was Sarah’s answer correct? It did not seem to help John completely. Where did the ,5 come from? Discuss. Try to explain why half = 0,5 on a calculator.
  • Which of you were wide awake? All of you? Did you all know? Wonderful! Yes, it’s because the calculator counts in tenths and five-tenths = one-half. The poor calculator has to use equivalent fractions to make tenths from things like halves and quarters and any fractions that are not tenths (hundredths and thousandths, but they come later).

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
hey
Giriraj
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
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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