A closed traverse has a total length of 774.662 m and a misclosure of -0.001 m in the easting and 0 m in the northing. What is the reciprocal of the precision of the survey? Provide your answer rounded to the nearest integer. E.g., if precision is 1/597.777853, its reciprocal rounded to the nearest integer should be 598

To calculate the reciprocal of the precision of the survey, we need to use the formula for the relative precision, which is based on the misclosure and the total traverse length.

The formula for precision is:

\[
\text{Precision} = \frac{\text{Total traverse length}}{\text{Misclosure distance}}
\]

### Step 1: Calculate the misclosure distance
The misclosure distance is the magnitude of the error, which can be found using the Pythagorean theorem:

\[
\text{Misclosure distance} = \sqrt{\left(\Delta E\right)^2 + \left(\Delta N\right)^2}
\]

Where:
- \(\Delta E\) is the misclosure in the easting direction (\(-0.001 \, \text{m}\))
- \(\Delta N\) is the misclosure in the northing direction (\(0 \, \text{m}\))

\[
\text{Misclosure distance} = \sqrt{(-0.001)^2 + (0)^2} = \sqrt{0.000001} = 0.001 \, \text{m}
\]

### Step 2: Calculate the precision
Now that we know the misclosure distance is \(0.001 \, \text{m}\) and the total traverse length is \(774.662 \, \text{m}\), we can compute the precision:

\[
\text{Precision} = \frac{774.662}{0.001} = 774662
\]

### Step 3: Find the reciprocal of the precision
The reciprocal of the precision is:

\[
\text{Reciprocal of precision} = \frac{1}{774662} \approx 1.29 \times 10^{-6}
\]

Since we are asked to round the reciprocal of the precision to the nearest integer, the reciprocal is approximately:

\[
774662
\]

Thus, the reciprocal of the precision of the survey is **774662**.

Would you like more details or further clarifications?

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Here are 5 related questions:
1. How do different types of surveying errors affect precision?
2. What other factors can lead to survey misclosure in practice?
3. How can misclosure be adjusted in a survey?
4. What is the significance of precision in geodetic surveying?
5. How does the precision of a closed traverse compare to other surveying methods?

**Tip:** Always double-check your measurements and calculations in surveying to minimize potential misclosures.

A closed traverse has a total length of 774.662 m and a misclosure of -0.001 m in the easting and 0 m in the northing. What is the reciprocal of the precision of the survey? Provide your answer rounded to the nearest integer.

This problem focuses on calculating the reciprocal of precision for a closed traverse with a total length of 774.662 m and a misclosure of -0.001 m in the easting. Learn how to apply precision and misclosure formulas in surveying, using the Pythagorean theorem. Suitable for college-level students.

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