≡Mathematics EN 9th grade: Real Numbers & Powers
1. Powers with integer exponents
- General rule:
\( a^n \) means multiplying 𝑎 by itself 𝑛 times
✔ Example:
\( 2^3 = 2 \times 2 \times 2 = 8 \)
- Zero exponent:
\( a^0 = 1 \), with \( a \neq 0 \)
✔ Example:
\( 5^0 = 1 \)
- Negative exponent:
\( a^{-n} = \frac{1}{a^n} \), with \( a \neq 0 \)
✔ Example:
\( 2^{-3} = \frac{1}{8} \)
- Rules important:
\( a^m \times a^n = a^{m+n} \)
\( \frac{a^m}{a^n} = a^{m-n} \)
\( (a^m)^n = a^{m \cdot n} \)
✔ Example:
\( 2^3 \times 2^2 = 2^5 = 32 \)
2. Scientific Notation
- Form:
\( a \times 10^n \), with \( 1 \leq a < 10 \)
✔ Examples
\( 3000 = 3 \times 10^3 \)
\( 0.004 = 4 \times 10^{-3} \)
3. Real Numbers and Decimals
- Real Numbers
Include: integers, rational and irrational numbers
- Decimals
✔ Finite decimal:
\( 0.5 = 1/2 \)
✔ Repeating decimal:
\( 0.333... = 1/3 \)
4. Operations with Real Numbers
- Order of operations:
Parentheses
Powers
Multiplication and division
Addition and subtraction
✔ Example:
\( 2 + 3 \times 4 = 2 + 12 = 14 \)
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