Class 10 Maths – Chapter 1 Revision Notes Real Numbers
(Latest NCERT Syllabus)
1. Real Numbers
All rational and irrational numbers together are called Real Numbers.
2. Rational Numbers
Numbers written in form p/q where q ≠ 0.
Examples: 3/5, -2, 0.75
3. Irrational Numbers
Numbers which cannot be written in form p/q.
Examples: √2, √5, π
4. Decimal Expansion of Rational Numbers
For a rational number p/q (after simplification):
(i) Terminating Decimal
If denominator contains only factors 2 and/or 5 then decimal expansion terminates.
Condition: q = 2^m × 5^n
Examples: 7/20 = 0.35, 11/125 = 0.088
(ii) Non-Terminating Recurring Decimal
If denominator contains factors other than 2 or 5.
Example: 7/9 = 0.777...
5. Important Facts
• Every terminating decimal is rational.
• Every recurring decimal is rational.
• Irrational numbers are non-terminating and non-recurring.
6. Representation on Number Line
Numbers like √2 and √3 can be represented on number line.
7. Important Solved Examples
Example 1: Check whether 13/250 is terminating.
250 = 2 × 5^3 → Terminating decimal.
Example 2: Check whether 7/12 is terminating.
12 = 2^2 × 3 → Non-terminating recurring decimal.
8. Important Questions for Practice
S.No Question
1 Define irrational numbers.
2 Is 0.25 rational?
3 Write one irrational number.
4 Is √9 rational or irrational?
5 Write decimal expansion of 1/8.
6 Is π rational?
(Latest NCERT Syllabus)
1. Real Numbers
All rational and irrational numbers together are called Real Numbers.
2. Rational Numbers
Numbers written in form p/q where q ≠ 0.
Examples: 3/5, -2, 0.75
3. Irrational Numbers
Numbers which cannot be written in form p/q.
Examples: √2, √5, π
4. Decimal Expansion of Rational Numbers
For a rational number p/q (after simplification):
(i) Terminating Decimal
If denominator contains only factors 2 and/or 5 then decimal expansion terminates.
Condition: q = 2^m × 5^n
Examples: 7/20 = 0.35, 11/125 = 0.088
(ii) Non-Terminating Recurring Decimal
If denominator contains factors other than 2 or 5.
Example: 7/9 = 0.777...
5. Important Facts
• Every terminating decimal is rational.
• Every recurring decimal is rational.
• Irrational numbers are non-terminating and non-recurring.
6. Representation on Number Line
Numbers like √2 and √3 can be represented on number line.
7. Important Solved Examples
Example 1: Check whether 13/250 is terminating.
250 = 2 × 5^3 → Terminating decimal.
Example 2: Check whether 7/12 is terminating.
12 = 2^2 × 3 → Non-terminating recurring decimal.
8. Important Questions for Practice
S.No Question
1 Define irrational numbers.
2 Is 0.25 rational?
3 Write one irrational number.
4 Is √9 rational or irrational?
5 Write decimal expansion of 1/8.
6 Is π rational?
