Visualisc 5.7,8,6 bar on the number
line with magnification,
Answers
We locate 4.
26
on the number line, by the process of
successive magnification. This has been illustrated in Figure.
Step 1: First we note that 4.
26
lies between 4 and 5
Step 2: Divide the portion between 4 and 5 into 10 equal
parts and use a magnifying glass to visualise that 4.
26
lies
between 4.2 and 4.3.
Step 3: Divide the portion between 4.2 and 4.3 into 10
equal parts and use a magnifying glass to visualise that 4.
26
lies between 4.262 and 4.263.
Step 5: Divide the portion between 4.262 and 4.263 into
10 equal parts and use a magnifying glass to visualise that 4.
26
lies between 4.2625 and 4.2627.
We note that 4.
26
is visualised closer to 4.263 than to 4.262.
The same procedure can be used to visualise a real number with a non-terminating and non-recurring decimal expansion on the number line to a required accuracy.
From the above discussions and visualisations we conclude again that every
real number is represented by a unique point on the number line. Further every point on the number line represents one and only one real number.
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