EXAMPLE 2 Find the quotient: \( \frac{2.4 \times 10^{7}}{9.6 \times 10^{3}} \). Divide the multipliers: \( 2.4 \div 9.6=0.25 \) Divide the powers of ten: \( \frac{10^{7}}{10^{3}}=10^{7-3}=10^{4} \) Combine the answers and write the product in scientific notation. \( 0.25 \times 10^{4}=0.25 \times\left(10 \times 10^{3}\right)=(0.25 \times 10) \times 10^{3}=2.5 \times 10^{3} \) EXERCISES \begin{tabular}{ll} Write each number in scientific notation. \( ( \) Lessons \( 2.2,2.3) \) \\ 1. \( 25,500,000 \) \\ Write each number in standard notation. \( ( \) Lessons \( 2.2,2.3) \) \\ 3. \( 5.23 \times 10^{4} \) \\ Simplify each expression. \( ( \) Lessons \( 2.1,2.4) \) \\ 5. \( (9-7)^{3} \cdot 5^{0}+(8+3)^{2} \) \\ 7. \( 3.2 \times 10^{5}+1.25 \times 10^{4}+2.9 \times 10^{5} \) & 4. \( 1.33 \times 10^{-5} \) \\ \hline\end{tabular}

Let's solve the exercises step by step. ### Exercise 1: Write \( 25,500,000 \) in scientific notation. To convert a number into scientific notation, we need to express it in the form \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer. 1. **Identify the significant figures**: The number \( 25,500,000 \) can be expressed as \( 2.55 \) (keeping two significant figures). 2. **Count the decimal places moved**: The decimal point in \( 2.55 \) is moved 7 places to the right to get back to \( 25,500,000 \). 3. **Write in scientific notation**: Thus, we have: \[ 25,500,000 = 2.55 \times 10^{7} \] ### Exercise 2: Write \( 5.23 \times 10^{4} \) in standard notation. To convert from scientific notation to standard notation, we move the decimal point to the right by the exponent's value. 1. **Move the decimal point**: Move the decimal point in \( 5.23 \) four places to the right: - \( 5.23 \) becomes \( 52300 \) after moving the decimal point four places. 2. **Write in standard notation**: Thus, we have: \[ 5.23 \times 10^{4} = 52300 \] ### Exercise 3: Simplify \( (9-7)^{3} \cdot 5^{0}+(8+3)^{2} \). 1. **Calculate \( (9-7)^{3} \)**: \[ (9-7)^{3} = 2^{3} = 8 \] 2. **Calculate \( 5^{0} \)**: \[ 5^{0} = 1 \] 3. **Combine the results**: \[ (9-7)^{3} \cdot 5^{0} = 8 \cdot 1 = 8 \] 4. **Calculate \( (8+3)^{2} \)**: \[ (8+3)^{2} = 11^{2} = 121 \] 5. **Final calculation**: \[ 8 + 121 = 129 \] ### Exercise 4: Simplify \( 3.2 \times 10^{5}+1.25 \times 10^{4}+2.9 \times 10^{5} \). 1. **Align the powers of ten**: Convert \( 1.25 \times 10^{4} \) to the same power as the others: \[ 1.25 \times 10^{4} = 0.125 \times 10^{5} \] 2. **Combine the terms**: \[ 3.2 \times 10^{5} + 0.125 \times 10^{5} + 2.9 \times 10^{5} = (3.2 + 0.125 + 2.9) \times 10^{5} \] 3. **Calculate the sum**: \[ 3.2 + 0.125 + 2.9 = 6.225 \] 4. **Final result**: \[ 3.2 \times 10^{5} + 1.25 \times 10^{4} + 2.9 \times 10^{5} = 6.225 \times 10^{5} \] ### Summary of Answers: 1. \( 25,500,000 = 2.55 \times 10^{7} \) 2. \( 5.23 \times 10^{4} = 52300 \) 3. \( (9-7)^{3} \cdot 5^{0}+(8+3)^{2} = 129 \) 4. \( 3.2 \times 10^{5}+1.25 \times 10^{4}+2.9 \times 10^{5} = 6.225 \times 10^{5} \)