Significant Concepts Related to Numbers

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1. Absolute Value and Modulus

Definition

The absolute value or modulus of a number refers to its distance from zero on the number line, irrespective of direction.

  • Represented by |x|.
  • If x is positive or zero, |x| = x.
  • If x is negative, |x| = -x (it becomes positive).

Examples

  • |5| = 5 (as 5 is already positive)
  • |-7| = 7 (as -7 is 7 units away from 0)
  • |0| = 0 (0 has no distance from itself)

Properties of Absolute Value

  1. |a × b| = |a| × |b|
    • Example: |-3 × 4| = 12 (same as |−3| × |4| = 3 × 4)
  2. |a/b| = |a| / |b| (b ≠ 0)
    • Example: |-8/2| = 4 (same as |−8| / |2| = 8 / 2)
  3. |a - b| represents the distance between a and b on the number line.
    • Example: |3 - 8| = 5 (distance between 3 and 8 is 5)

MCQs on Absolute Value

1. What is the absolute value of -12?

a) -12

b) 12

c) 0

d) -6

✅ Answer: b) 12

2. Which of the following is true?

a) | -7 | = -7

b) | -10 | + |5| = -5

c) | -8 | = |8|

d) | 0 | = 1

✅ Answer: c) | -8 | = |8|

2. Successor and Predecessor

Definition

  • Successor of a number n is n + 1 (the next number).
  • Predecessor of a number n is n - 1 (the previous number).

Examples

  • Successor of 8 → 8 + 1 = 9
  • Predecessor of 15 → 15 - 1 = 14
  • Successor of -5 → -5 + 1 = -4
  • Predecessor of 0 → 0 - 1 = -1

MCQs on Successor and Predecessor

3. What is the successor of 99?

a) 98

b) 100

c) 101

d) 97

✅ Answer: b) 100

4. What is the predecessor of -12?

a) -11

b) 11

c) -13

d) 13

✅ Answer: c) -13

3. Order of Numbers (Ascending & Descending)

Definition

  • Ascending Order: Arranging numbers from smallest to largest.
    • Example: 3, 7, 12, 18, 25
  • Descending Order: Arranging numbers from largest to smallest.
    • Example: 50, 40, 30, 20, 10

Steps for Ordering Numbers

  1. Compare the place values of digits.
  2. Arrange accordingly based on ascending/descending order.

Examples

  • Arrange 25, 9, 43, 17, 31 in ascending order:
    • 9, 17, 25, 31, 43
  • Arrange 10, 55, 3, 27, 81 in descending order:
    • 81, 55, 27, 10, 3

MCQs on Ordering Numbers

5. Which of the following is correctly arranged in ascending order?

a) 10, 8, 15, 3

b) 2, 7, 12, 20

c) 50, 40, 30, 20

d) 9, 5, 2, 1

✅ Answer: b) 2, 7, 12, 20

6. Arrange 14, 28, 7, 35 in descending order.

a) 7, 14, 28, 35

b) 35, 28, 14, 7

c) 14, 7, 28, 35

d) 35, 28, 7, 14

✅ Answer: b) 35, 28, 14, 7

4. Scientific Notation (Standard Form of Numbers)

Definition

Scientific notation is a way to express very large or very small numbers in the form:

N×10pN×10p

where:

  • N is a number between 1 and 10.
  • p is the power of 10.

Conversion to Scientific Notation

  1. Move the decimal point to get a number between 1 and 10.
  2. Count the number of places the decimal moved.
    • If moved left, power is positive.
    • If moved right, power is negative.

Examples

  • 25000 → 2.5 × 10⁴ (moved decimal 4 places left)
  • 0.0042 → 4.2 × 10⁻³ (moved decimal 3 places right)
  • 5,678,000 → 5.678 × 10⁶

MCQs on Scientific Notation

7. What is 0.0009 in scientific notation?

a) 9 × 10³

b) 9 × 10⁻³

c) 9 × 10⁻⁴

d) 90 × 10⁻³

✅ Answer: c) 9 × 10⁻⁴

8. Express 760000 in scientific notation.

a) 7.6 × 10⁵

b) 76 × 10⁶

c) 0.76 × 10⁶

d) 7.6 × 10⁶

✅ Answer: a) 7.6 × 10⁵

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