Determine the following estimate without using a calculator. Then use a calculator to perform the computation necessary to obtain an exact answer. How reasonable is your estimate when compared to the actual​ answer?
A raise of ​$290 comma 000 is evenly distributed among 301 professors. Estimate the amount each professor receives.
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Part 1
The estimate of the amount each professor receives is approximately ​$
  
enter your response here.
​(Round to the nearest thousand as​ needed.)

### Estimation:

We are asked to distribute $290,000 evenly among 301 professors. First, we can round both the total amount and the number of professors to make the calculation simpler.

- Approximate the total amount: 
  \[
  290,000 \approx 300,000
  \]
- Approximate the number of professors:
  \[
  301 \approx 300
  \]

Now, divide the rounded values:
\[
\frac{300,000}{300} = 1,000
\]

So, the estimate is that each professor would receive approximately **$1,000**.

---

### Exact Calculation:

Now, let's calculate the exact amount using a calculator:
\[
\frac{290,000}{301} \approx 964.12
\]

### Comparison:

- **Estimated amount**: $1,000
- **Exact amount**: $964.12

The estimate of $1,000 is reasonable and quite close to the exact value of $964.12. The difference is about $36, which is small compared to the total amount being distributed.

---

Do you want more details, or have any questions?

Here are 5 related questions to expand on this concept:
1. How does rounding affect the precision of calculations in real-life scenarios?
2. What methods can improve accuracy when estimating large divisions?
3. How can we check if a rounding approximation is close enough to the exact answer?
4. What happens when you distribute a raise unevenly? How would you calculate that?
5. How would rounding to different significant digits affect other real-life problems?

**Tip**: Rounding to the nearest hundred or thousand often simplifies mental math while keeping the result fairly accurate!

Determine the following estimate without using a calculator. Then use a calculator to perform the computation necessary to obtain an exact answer. How reasonable is your estimate when compared to the actual​ answer? A raise of $290,000 is evenly distributed among 301 professors. Estimate the amount each professor receives.

Learn how to estimate the distribution of a $290,000 raise among 301 professors by rounding and dividing. Get step-by-step solutions to compare the estimate with the exact calculation. Suitable for students in Grades 6-8.

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