What is a Number Line?

  • A number line is a straight, horizontal line used to visually represent numbers.
  • It includes positive numbers, negative numbers, and zero.
  • It is divided into equal parts using tick marks.

Structure of the Number Line

  • Zero (0) is at the center of the number line.
  • Positive values lie to the right of zero.
  • Negative values lie to the left of zero.
  • The line extends infinitely in both directions.
  • Arrows are placed at both ends to show infinity.

Positive Values

  • Positive numbers are greater than zero.
  • Examples: 1, 2, 3, 10, 100
  • They are always located to the right of zero on the number line.
  • The farther right a number is, the greater it is in value.

Negative Values

  • Negative numbers are less than zero.
  • Examples: −1, −2, −5, −100
  • They are always placed to the left of zero on the number line.
  • The farther left a number is, the smaller it is in value.

Zero on the Number Line

  • Zero (0) is the central reference point.
  • It is neither positive nor negative.
  • Used to compare direction and magnitude of values.

Distance from Zero

  • Absolute value of a number is its distance from zero.
  • Example: |−3| = 3, |4| = 4
  • Two numbers equidistant from zero but in opposite directions are called opposites.

Comparison on the Number Line

  • A number to the right is always greater than a number to the left.
  • Example: 3 > −1, 0 > −10, 5 > 2
  • This is helpful in ordering, sorting, and evaluating expressions.

Applications in Arithmetic

  • Used in visualizing addition and subtraction:
  • Addition: move right
  • Subtraction: move left
  • Example: 2 − 5 = −3 (start from 2, move 5 steps left)

Usage in Exam Topics

  • Used in number system, integers, rational numbers, simplification
  • Appears in SSC CGL, CHSL, Banking Prelims, RRB NTPC
  • Questions like “Which number is greater?”, “Find opposite number”, “Add or subtract using line” are common.

Examples of Positioning

  • −3 lies to the left of −2, so it is smaller
  • +4 lies to the right of +1, so it is greater
  • −1 is to the left of 0

Real-Life Applications

  • Banking (e.g., overdrafts as negative values)
  • Temperature scales (e.g., −5°C is colder than 0°C)
  • Elevations below sea level (−100 m)

Miscellaneous Points

  • Can represent both discrete values (like integers) and continuous values (like decimals)
  • Helpful for visual learners to understand positive and negative interactions
  • Often used in coordinate geometry and graph plotting

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