Magnification of Number line

Hi,

Today I’m going to explain “Magnification of Decimal numbers on number lines”.

Number line

   A line which is used to express the location of any thing in one dimension or I can say only a horizontal line of Cartesian plane.

Now I’m going to take these representation to further steps i.e.
Representing Decimals up to one place two or three or more places.

How to Represent Decimal expansion up to three place i.e. 10th place on number line :

Magnify
    Before starting this phase I want to clear that each numbers or decimals has base as 10 or briefly I should say, in standard form of number system of Maths works by taking 10 as base, so that’s mean if I’m taking 1 and 2 that means there exist 10 such numbers between 1 and 2 i.e. 1.1, 1.2, 1.3…………1.9, 2.0 that is up to 10th place.
And if we look up to 100th number that means those 1 and 2 can have 100 numbers i.e. 1.01, 1.02, 1.03……1.11, 1.12, 1.13……1.98, 1.99, 2.00.

And if it is up to three places i.e. 1000th place then those 1 and 2 will have 1000 such numbers i.e. 1.001, 1.002 and so on.

   On the aspect of representation on number line one should start with 10th place for example :-

Q. Represent on number line 1.345.

Sol.   first of all we’ll have to decide between what numbers 1.345 will fall
yes, of course it will fall between 1 and 2 and the number given is 1000th place type.
 

0—–1—–2—–3—–4—–5—–6—–7—–8—–9

now we will have to divide the gap of 1 and 2 in 10 equal parts and each will represent 1.1, 1.2, 1.3…..1.9 and 2.00 or 2 look at below
line –

0———-1—1.1—1.2—1.3—1.4—1.5—1.6—1.7—1.8—1.9—2—————3

now we have clear picture of magnification of line up to to 10th place and we have to represent 1.345 that means we will have to further magnifies the gap of 1.3 i.e 1.30 and 1.4 i.e 1.40 because the next stage of location is 1.34

1.3—1.31—1.32—133—1.34—1.35—1.36–1.37

at the last for 1000th place i.e. 1.345 we’ll repeat the same step i.e. further magnifying 1.34 and 1.35, as I’ve already mentioned that each magnification step will magnifies for 10 places, so it will remain same.
As we are looking forward to magnifies the gap of 1.34 to 1.35 this is clearly mean that we are magnifying 1.340 to 1.350.
Definitely there can be 10 numbers such that 1.341, 1.342, 1.343……..1.350 hence look at below –

1.340—-1.341……….—1.344—1.345……..1.350

this is the required location.
Try some other numbers or try these

  • 2.34
  • 3.762
  • 9.012
  • 5.1076

Hence this is all for magnification of number line, still if you are finding difficulties then feel free to comment.

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About the Author: Faizan

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