Chapter 1 · Class 10 CBSE · Formula Sheet
Real Numbers Formulas — Class 10 CBSE
Apply Euclid's division lemma and fundamental theorem of arithmetic to HCF, LCM, and irrationality proofs.
Key Formulas
Euclid's Division Lemma
a = bq + r, \quad 0 \leq r < b
Fundamental Theorem of Arithmetic
\text{Every composite number} = p_1^{a_1} \times p_2^{a_2} \times \cdots \times p_n^{a_n}
HCF-LCM Relation
\text{HCF}(a,b) \times \text{LCM}(a,b) = a \times b
Irrational Proof Method
\text{Prove by contradiction that } \sqrt{p} \text{ is irrational for prime } p
Terminating Decimal
\dfrac{p}{q} \text{ terminates if } q = 2^m \times 5^n
Worked Examples
1Using: Place Value
Find the place value of 6 in 3,65,421.
Step 1: 6 is in the ten-thousands place.
Step 2: Place value = 6 x 10,000 = 60,000.
Answer: 60,000
2Using: Successor
Find the successor of 9,999.
Step 1: Successor = n + 1
Step 2: = 9,999 + 1 = 10,000.
Answer: 10,000
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