visualise 1.835 on the number line using successive magnification
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we will proceed by successive magnification process.we know that
i.e. in the interval [ 1,2 ] and have a rough idea where it is located on the number line. To get a more accurate estimation of the representation,we divide the interval [ 1,2 ] into 10 equal parts and look at [ 1.8 , 1.9 ] through a magnifying glass and realize that 1.835 lies between 1.8 and 1.9 , i.e. , in the interval [ 1.8, 1.9 ] .
Now we may imagine that each of the new internal [ 1 , 1.1 ] , [ 1.1 ,1.2 ] , [ 1.2 , 1.3 ] , .......[ 1.9 ,2] has been sub - divided into 10 equal parts.
As before, we can now visualize through the magnifying glass that 1.835 lies in the interval [ 1.83 , 1.84 ]
plzzz see the above pic....
Hence, we observe that it is possible by sufficient successive magnification to visualize the position of a real number with a terminating decimal expansion on the number line.
Step -1. The given number line between 1 and 2 .
step -2.magnifying the interval between 1 and 2.
Step-3. The given number lies between 1.8 and 1.9 .
step -4. Divine the interval 1.8 and 1.9 into ten equal parts and magnify it.
step -5. The given number lies between 1.83 and 1.84 .
Step -6. magnify the interval between 1.83 and 1.84 and divide it into ten equal parts.
step -7. 1.835 is the fifth division in the magnification.
____________________________
☺☺
I hope this will be helpful for you dear ...★
________________________________
we will proceed by successive magnification process.we know that
i.e. in the interval [ 1,2 ] and have a rough idea where it is located on the number line. To get a more accurate estimation of the representation,we divide the interval [ 1,2 ] into 10 equal parts and look at [ 1.8 , 1.9 ] through a magnifying glass and realize that 1.835 lies between 1.8 and 1.9 , i.e. , in the interval [ 1.8, 1.9 ] .
Now we may imagine that each of the new internal [ 1 , 1.1 ] , [ 1.1 ,1.2 ] , [ 1.2 , 1.3 ] , .......[ 1.9 ,2] has been sub - divided into 10 equal parts.
As before, we can now visualize through the magnifying glass that 1.835 lies in the interval [ 1.83 , 1.84 ]
plzzz see the above pic....
Hence, we observe that it is possible by sufficient successive magnification to visualize the position of a real number with a terminating decimal expansion on the number line.
Step -1. The given number line between 1 and 2 .
step -2.magnifying the interval between 1 and 2.
Step-3. The given number lies between 1.8 and 1.9 .
step -4. Divine the interval 1.8 and 1.9 into ten equal parts and magnify it.
step -5. The given number lies between 1.83 and 1.84 .
Step -6. magnify the interval between 1.83 and 1.84 and divide it into ten equal parts.
step -7. 1.835 is the fifth division in the magnification.
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