The number line is a fundamental tool for visualising real numbers. In the CBSE Class 10 curriculum, students learn to position all types of real numbers — integers, fractions, terminating decimals, non-terminating recurring decimals, and even irrational numbers — on the number line using systematic methods.
Integers are plotted at evenly spaced points on the number line. To plot fractions like 3/5, divide the segment between 0 and 1 into 5 equal parts and mark the third division. Negative fractions are plotted similarly to the left of 0.
To plot a decimal like 2.665 on the number line: (1) Locate 2.6 between 2 and 3 by dividing into 10 equal parts. (2) Magnify the segment between 2.6 and 2.7 into 10 parts to locate 2.66. (3) Magnify again to locate 2.665. This technique of successive magnification lets you locate any terminating decimal with any number of decimal places.
To plot √2: (1) Draw a unit square on the number line starting at 0. (2) The diagonal of this square has length √2 (by the Pythagorean theorem: 1² + 1² = 2). (3) Using a compass centred at the origin, swing an arc from the end of the diagonal to the number line. The point where the arc meets the number line represents √2. This technique generalises to √n using the spiral of Theodorus.
The real number line is complete — every point on the line corresponds to a unique real number and every real number has a unique point. This means there are no "gaps" on the number line. Between any two real numbers, there are infinitely many rational numbers and infinitely many irrational numbers.
Draw a right triangle with both legs of length 1 starting at the origin on the number line. The hypotenuse has length √2. Use a compass to swing the hypotenuse down to the number line to mark √2.
Successive magnification is a method of zooming in on a section of the number line to locate a decimal more precisely. You repeatedly divide a segment into 10 equal parts to place each subsequent decimal digit.
Yes. Every real number (rational or irrational) corresponds to exactly one point on the number line. This is the completeness property of real numbers.
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