# 3.3 Recognise, classify, represent and describe numbers

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## To recognise and use equivalent forms of numbers [lo 1.5.2]

1. You have just completed a learning unit on ordinary fractions. Let us do some revision.

What fraction in each of the following figures is coloured in?

1.1

1.2

1.3

2. Write the answers above as decimal fractions.

## Tenths

We read 0,3 as nought comma three and we call it a decimal fraction .

The comma is called the decimal sign and it separates the whole numbers from the fractions.

Do you still remember?

$\frac{1}{\text{10}}$

3. Look at the number line and fill in the missing numbers.

4. Work together with a friend. Count aloud and complete the following:

4.1 0,2 ; 0,4 ; 0,6 ; .............. ; .............. ; .............. ; .............. ; .............. ;

4.2 4,7 ; 4,5 ; 4,3 ; .............. ; .............. ; .............. ; .............. ; .............. ;

4.3 0,5 ; 1,5 ; .............. ; .............. ; .............. ; .............. ; .............. ;

4.4 3,6 ; 3,2 ; .............. ; .............. ; .............. ; .............. ; .............. ;

4.5 9,2 ; 9,1 ; .............. ; .............. ; .............. ; .............. ; .............. ;

Do you still remember?

If I want to add 0,3 to the previous number repeatedly I can programme my calculator in this way: Number + 0,3 + = = =

## To use a series of techniques to do mental arithmetic [lo 1.10.5]

By now you know that we can use the pocket calculator very effectively to find or check answers. Now that you have seen how to programme your pocket calculator or to add on, try to complete the following activity without making any mistakes. Programme your pocket calculator and write the first 10 answers to the following:

1.1 Start at 3,7 and add 0,6 each time:

1.2 Start at 9,3 and subtract 0,4 each time:

## Activity 3:

• To recognise, classify and represent numbers in order to describe and compare them [LO 1.3.3]
• To recognise and use equivalent forms of numbers [LO 1.5.2]
• To use a series of techniques to do mental arithmetic [LO 1.10.5]

In this activity we would like to see whether you can determine which ordinary fractions (mixed numbers) fit in with which decimal fractions. It is important for you to be able to see that 0,2kg is actually exactly the same as $\frac{2}{\text{10}}$ kg !

1. Link the ordinary fractions to their decimal fraction partners. Connect column A to the correct answer in column B.

 A B E.g. 0,2 kg 1 $\frac{5}{\text{10}}$ / 1 $\frac{1}{2}$ km 1.1 0,5 m 152 $\frac{7}{\text{10}}$ km 1.2 17,6 litre $\frac{2}{\text{10}}$ kg 1.3 8,4 seconds 8 $\frac{4}{\text{10}}$ sec 1.4 152,7 km 17 $\frac{6}{\text{10}}$ ℓ 1.5 1,5 km $\frac{5}{\text{10}}$ / $\frac{1}{2}$ m

Challenge!

2. Work with a friend. Write the following fractions as decimal fractions:

2.1 $\frac{4}{5}$ 2.2 $\frac{2}{\text{20}}$

2.3 $\frac{3}{5}$ 2.4 $\frac{7}{\text{20}}$

2.5 $\frac{\text{18}}{\text{30}}$ 2.6 $\frac{\text{48}}{\text{60}}$

3. Explain what must be done to get the above answers.

5. Now use a calculator to check your answers in no. 2.

## To be capable of doing mental arithmetic [lo 1.9]

1. You now have the opportunity of improving your mental arithmetic skills and applying your newly acquired knowledge. Complete the following mental arithmetic test as quickly and as accurately as possible:

find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
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salma
Commplementary angles
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Sherica
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Sherica
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Tamia
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Uday
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salma
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or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
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Cied
types of nano material
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Porter
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Porter
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Yasmin
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Cesar
I'm interested in nanotube
Uday
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what is system testing
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Stotaw
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Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
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Azam
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Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
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
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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