1. The seamstress needs a 2 yards long cloth for the skirt she's sewing. So she asked her niece to cut it from their stock. Upon receiving she tried to measure it. Using her meter stick she measured the cloth at 2.25 meters a) Find the percent error?(8pts)

To find the percent error, we can use the following formula: \[ \text{Percent Error} = \left( \frac{\text{Measured Value} - \text{True Value}}{\text{True Value}} \right) \times 100 \] In this case: - **True Value** (the length of cloth needed) = 2 yards - **Measured Value** (the length of cloth measured) = 2.25 meters First, we need to convert the true value from yards to meters. We know that: 1 yard = 0.9144 meters So, to convert 2 yards to meters: \[ 2 \text{ yards} \times 0.9144 \text{ meters/yard} = 1.8288 \text{ meters} \] Now we can substitute the values into the percent error formula: \[ \text{Percent Error} = \left( \frac{2.25 \text{ meters} - 1.8288 \text{ meters}}{1.8288 \text{ meters}} \right) \times 100 \] Calculating the difference: \[ 2.25 - 1.8288 = 0.4212 \text{ meters} \] Now, substituting this back into the formula: \[ \text{Percent Error} = \left( \frac{0.4212}{1.8288} \right) \times 100 \] Calculating the fraction: \[ \frac{0.4212}{1.8288} \approx 0.230 \] Now, multiplying by 100 to get the percent: \[ 0.230 \times 100 \approx 23.0\% \] Thus, the percent error is approximately **23.0%**.