Chapter 1 · Class 9 CBSE · Formula Sheet
Number Systems Formulas — Class 9 CBSE
Classify numbers into naturals, integers, rationals, and irrationals; represent on number line.
Key Formulas
Irrational Numbers
\sqrt{2}, \sqrt{3}, \sqrt{5}, \pi \text{ are irrational}
Rationalizing Denominator
\dfrac{1}{\sqrt{a}} = \dfrac{\sqrt{a}}{a}
Rationalizing (Binomial)
\dfrac{1}{a + \sqrt{b}} = \dfrac{a - \sqrt{b}}{a^2 - b}
Laws of Exponents
a^m \cdot a^n = a^{m+n}, \quad \dfrac{a^m}{a^n} = a^{m-n}, \quad (a^m)^n = a^{mn}
Fractional Exponent
a^{1/n} = \sqrt[n]{a}
Negative Exponent
a^{-n} = \dfrac{1}{a^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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