8.54. Write the following numbers in scientific notation. \( \begin{array}{ll}\text { a. } 370,000,000 & \text { b. } 7,600\end{array} \)

To convert numbers into scientific notation, we express them in the form \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer. Let's solve each part step by step. ### a. Converting 370,000,000 to scientific notation 1. **Identify the significant figures**: The significant figures in 370,000,000 are 3.7. 2. **Count the decimal places moved**: We move the decimal point 8 places to the left to get from 370,000,000 to 3.7. 3. **Write in scientific notation**: Therefore, we can express 370,000,000 as: \[ 3.7 \times 10^8 \] ### b. Converting 7,600 to scientific notation 1. **Identify the significant figures**: The significant figures in 7,600 are 7.6. 2. **Count the decimal places moved**: We move the decimal point 3 places to the left to get from 7,600 to 7.6. 3. **Write in scientific notation**: Therefore, we can express 7,600 as: \[ 7.6 \times 10^3 \] ### Final Answers - a. \( 370,000,000 = 3.7 \times 10^8 \) - b. \( 7,600 = 7.6 \times 10^3 \)