Solve the following . observing significant figure rules 125stimes 45.3m/s 6times 10^3m 5.7times 10^3m 5662.5 m 5.66times 10^3m

To solve the problem while observing significant figure rules, we need to consider the number of significant figures in each value involved in the calculations.<br /><br />1. **Multiplication: \(125 \, \text{s} \times 45.3 \, \text{m/s}\)**<br /><br /> - The number 125 has 3 significant figures.<br /> - The number 45.3 has 3 significant figures.<br /> - When multiplying, the result should have the same number of significant figures as the factor with the fewest significant figures, which is 3 in this case.<br /><br /> Calculation:<br /> \[<br /> 125 \times 45.3 = 5662.5<br /> \]<br /><br /> Rounding to 3 significant figures:<br /> \[<br /> 5660 \quad (\text{rounded to 3 significant figures})<br /> \]<br /><br />2. **Scientific Notation: \(6 \times 10^{3} \, \text{m}\) and \(5.7 \times 10^{3} \, \text{m}\)**<br /><br /> - The number \(6 \times 10^{3}\) has 1 significant figure.<br /> - The number \(5.7 \times 10^{3}\) has 2 significant figures.<br /><br />3. **Given Values:**<br /><br /> - The number 5662.5 m is given with 5 significant figures.<br /> - The number \(5.66 \times 10^{3} \, \text{m}\) has 3 significant figures.<br /><br />In summary, when performing operations, ensure that the final answer reflects the correct number of significant figures based on the initial values used in the calculation. For the multiplication example provided, the result rounded to the appropriate number of significant figures is 5660.