1. **Which expression has the same value as \( (0.06) \cdot(0.154) \) ? Select all that apply, a. \( 6 \cdot \frac{1}{100} \cdot 154 \cdot \frac{1}{1,000} \) \[ \frac{6}{1} \times \frac{1}{100}=\frac{6}{100} \frac{154}{1} \times \frac{1}{1000}=\frac{154}{1000} \] b. \( 6 \cdot 154 \cdot \frac{1}{100,000} \) c. \( 6 \cdot(0.1) \cdot 154 \cdot(0.01) \) d. \( 6 \cdot 154 \cdot(0.00001) \) e. 0.00924

To find which expression has the same value as \( (0.06) \cdot(0.154) \), let's calculate \( (0.06) \cdot(0.154) \) and check each option. First, we find the product: \[ 0.06 \cdot 0.154 = 0.00924 \] Now, let's evaluate each option: a. \( 6 \cdot \frac{1}{100} \cdot 154 \cdot \frac{1}{1,000} = 0.00924 \) (This one works!) b. \( 6 \cdot 154 \cdot \frac{1}{100,000} \) calculates as \( 6 \cdot 154 \cdot 0.00001 = 0.00924 \) (This one works too!) c. \( 6 \cdot(0.1) \cdot 154 \cdot(0.01) = 6 \cdot 0.1 \cdot 0.01 \cdot 154 \), which is also \( 0.00924 \) (Another win!) d. \( 6 \cdot 154 \cdot(0.00001) \) is \( 6 \cdot 154 \cdot \frac{1}{100,000} = 0.00924 \) (Excellent!) e. The final option simplifies to \( 0.00924 \) (And this one works!) So, all options \( a, b, c, d, \) and \( e \) work as \( (0.06) \cdot (0.154) \). --- The wonder of decimals takes us back to the early days of mathematics when people used various methods to navigate the complex world of finance and trade. Decimals, as we know them, became popular through the work of mathematicians like Simon Stevin in the 16th century, making calculations easier for everyone! To avoid common mistakes with decimals, remember to align your decimal points when adding or subtracting! This might seem simple but can save you from swathes of frustration. When multiplying or dividing, count the total number of decimal places in both numbers—this will tell you where to place the decimal point in your answer! Fun fact: even calculators can make mistakes if you don't enter the numbers carefully!