Assume that all numbers are approximate. ​(a) Estimate the result and ​(b) perform the indicated operations on a calculator and compare with the estimate.
3894/500.1-2.028*308.9/378.9

### (a) **Estimate the result:**

Let's break down the calculation and estimate:

\[
\frac{3894}{500.1} - \frac{2.028 \times 308.9}{378.9}
\]

First, estimate each term individually:

1. **Estimate** \(\frac{3894}{500.1}\):  
   \[
   \frac{3894}{500.1} \approx \frac{3900}{500} = 7.8
   \]
   
2. **Estimate** \(\frac{2.028 \times 308.9}{378.9}\):  
   \[
   2.028 \times 308.9 \approx 2 \times 310 = 620
   \]  
   \[
   \frac{620}{378.9} \approx \frac{620}{380} = 1.63
   \]

Now subtract:
\[
7.8 - 1.63 \approx 6.17
\]

### (b) **Perform the exact calculation:**

Now let's compute the expression precisely.

1. Compute \(\frac{3894}{500.1}\).
2. Compute \(2.028 \times 308.9\), then divide by 378.9.
3. Subtract the results.

I'll do the calculation now.The exact result of the calculation is approximately **6.13**.

### Comparison:
- **Estimated result**: 6.17
- **Exact result**: 6.13

The estimate is quite close to the exact value.

---

Would you like further clarification or details on any part of the process?

Here are 5 related questions to explore:

1. What are the rules of significant figures in estimations?
2. How can rounding affect the final result in complex expressions?
3. Why is estimating important before performing precise calculations?
4. How can you improve the accuracy of mental estimates?
5. Can small differences in values significantly affect calculations?

**Tip**: Estimating intermediate steps can help catch errors before final calculations are made.

Estimate the result and perform the indicated operations on a calculator: 3894/500.1 - 2.028 * 308.9 / 378.9

Learn how to estimate and accurately compute the expression 3894/500.1 - 2.028 * 308.9/378.9. This step-by-step guide demonstrates how to simplify arithmetic operations, including division and multiplication, and how estimation can help verify results. Suitable for students in Grades 6-8.

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