3 Omar measures one machine part with length 4.392 centimeters and another part with length 6.82 centimeters. What is the difference in length? Use estimation to check your answer for reasonableness

To find the difference in length between the two machine parts measured by Omar, follow these steps: ### 1. Calculate the Exact Difference **Measurements:** - Part 1: 4.392 centimeters - Part 2: 6.82 centimeters **Calculation:** \[ \text{Difference} = \text{Part 2} - \text{Part 1} = 6.82 \, \text{cm} - 4.392 \, \text{cm} = 2.428 \, \text{cm} \] So, the exact difference in length is **2.428 centimeters**. ### 2. Estimate to Check Reasonableness Estimation helps verify that the calculated difference is reasonable by simplifying the numbers: **Rounding the Measurements:** - **Part 1:** 4.392 cm ≈ **4.4 cm** (rounded to one decimal place) - **Part 2:** 6.82 cm ≈ **6.8 cm** (rounded to one decimal place) **Estimated Difference:** \[ \text{Estimated Difference} = 6.8 \, \text{cm} - 4.4 \, \text{cm} = 2.4 \, \text{cm} \] **Comparison:** - **Exact Difference:** 2.428 cm - **Estimated Difference:** 2.4 cm The estimated difference (**2.4 cm**) is very close to the exact difference (**2.428 cm**), which confirms that the calculated value is reasonable. ### Conclusion - **Exact Difference:** 2.428 centimeters - **Estimated Difference:** 2.4 centimeters The estimation aligns well with the exact calculation, indicating that the difference of **2.428 centimeters** is a reasonable and accurate measurement.