Measurement and error: the upper limit of the length of a wire ie 4.85 m. When it is equally divided into x pieces, the least  possible length of each piece is 28.5 cm. Find the greatest possible value of n.

To find the greatest possible value of \( n \) (the number of pieces), we start by noting the given measurements:

1. The upper limit of the length of the wire is \( 4.85 \) m.
2. The least possible length of each piece is \( 28.5 \) cm.

First, we convert the upper limit of the wire from meters to centimeters:

\[
4.85 \, \text{m} = 485 \, \text{cm}
\]

Next, we need to determine how many pieces of length at least \( 28.5 \) cm can fit into \( 485 \) cm. To do this, we divide the total length of the wire by the least possible length of each piece:

\[
n = \frac{485 \, \text{cm}}{28.5 \, \text{cm}} \approx 17.0175
\]

Since \( n \) must be a whole number, we take the greatest integer less than or equal to \( 17.0175 \):

\[
n = 17
\]

Thus, the greatest possible value of \( n \) is \( 17 \).

### Summary
- **Greatest possible value of \( n \):** 17

Would you like further details or explanations? Here are some related questions you might find interesting:

1. How do you calculate the error margin in measurements?
2. What is the concept of significant figures in measurements?
3. How would the result change if the least length of each piece was different?
4. Can you explain the difference between absolute and relative error?
5. What are practical applications of measurement and error in engineering? 

**Tip:** Always ensure that all units are consistent before performing calculations.

Measurement and error: the upper limit of the length of a wire ie 4.85 m. When it is equally divided into x pieces, the least possible length of each piece is 28.5 cm. Find the greatest possible value of n.

Discover how to find the maximum number of pieces a 4.85 m wire can be divided into, with each piece measuring at least 28.5 cm. This detailed solution explains the steps and concepts involved in measurement and division. Ideal for students in Grades 7-9.

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