🌟 CBSE Class 10 Maths – Chapter 1: REAL
NUMBERS 🌟
🎯 Board Exam Creative Notes
✨ Chapter Overview
This chapter teaches:
✅ Euclid’s Division Lemma
✅ Fundamental Theorem of Arithmetic
✅ HCF & LCM
✅ Irrational Numbers
✅ Decimal Expansion of Rational Numbers
📌 Very Important for Boards because:
• Short proofs are asked frequently.
• Case-study & MCQs come every year.
• 2–3 mark questions are common.
🔵 1. REAL NUMBERS
📖 Definition
All numbers that can be represented on the number line are called Real Numbers.
Types of Real Numbers
Real Numbers
/
Rational Numbers Irrational Numbers
🔹 Rational Numbers
Numbers written in the form:
1
, p
,q 0 =
q
Examples:
✅2
✅ -5/7
✅ 0.25
🔹 Irrational Numbers
p
Numbers that cannot be written in q form.
Examples:
✅ √2
✅ √3
✅π
🟣 2. EUCLID’S DIVISION LEMMA
📖 Statement
For any two positive integers a and b:
a = bq + r
where:
•0 ≤r<b
• a = Dividend
• b = Divisor
• q = Quotient
• r = Remainder
🎨 Trick to Remember
🌈 “D-D-Q-R”
Dividend = Divisor × Quotient + Remainder
2
NUMBERS 🌟
🎯 Board Exam Creative Notes
✨ Chapter Overview
This chapter teaches:
✅ Euclid’s Division Lemma
✅ Fundamental Theorem of Arithmetic
✅ HCF & LCM
✅ Irrational Numbers
✅ Decimal Expansion of Rational Numbers
📌 Very Important for Boards because:
• Short proofs are asked frequently.
• Case-study & MCQs come every year.
• 2–3 mark questions are common.
🔵 1. REAL NUMBERS
📖 Definition
All numbers that can be represented on the number line are called Real Numbers.
Types of Real Numbers
Real Numbers
/
Rational Numbers Irrational Numbers
🔹 Rational Numbers
Numbers written in the form:
1
, p
,q 0 =
q
Examples:
✅2
✅ -5/7
✅ 0.25
🔹 Irrational Numbers
p
Numbers that cannot be written in q form.
Examples:
✅ √2
✅ √3
✅π
🟣 2. EUCLID’S DIVISION LEMMA
📖 Statement
For any two positive integers a and b:
a = bq + r
where:
•0 ≤r<b
• a = Dividend
• b = Divisor
• q = Quotient
• r = Remainder
🎨 Trick to Remember
🌈 “D-D-Q-R”
Dividend = Divisor × Quotient + Remainder
2
