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Suppose you have a book on the counter, and you decide to estimate the thickness of each sheet. You use a ruler that is graduated in millimeters and determine that the length from the front cover to the back cover is 2.6 cm. Furthermore, you notice that the last page number is 328, indicating the book has 328 pages.

How thick do you predict each sheet of the book is?

Note:
- The number of "sheets" is the number of "leaves" or physical pieces of paper that are bound to make the book.
- Each sheet or piece of paper has both a front side and a backside. Each side is a unique page.
- This means that each "sheet" consists of two pages.
- For this problem, assume the front cover and the back cover are equal in thickness to the sheet thicknesses in between.

Give your answer in units of centimeters, but DO NOT include the letters "cm" in your answer. Only include the numerical portion in the answer box; otherwise, the answer (even if correct) will be counted as incorrect. Keep three decimal places in your answer.

Answer :

The thickness of each sheet in a book that is 2.6 cm thick with 328 pages is calculated by dividing the total book thickness by half the number of pages to account for each sheet having two pages. After the division and conversion from millimeters to centimeters, the thickness per sheet is approximately 0.016.

To predict the thickness of each sheet in the book, we first need to consider that the book is 2.6 cm thick and contains 328 pages. Since each sheet consists of two pages, the book has 164 sheets. We can calculate the thickness of each sheet by dividing the total thickness of the book by the number of sheets.

The calculation is as follows:

Convert the book's thickness to millimeters:

2.6 cm = 26 mm (since 1 cm = 10 mm).

Divide this number by the number of sheets:

26 mm / 164 sheets

= 0.158536585 mm per sheet.

Convert the sheet thickness back to centimeters:

0.158536585 mm = 0.0158536585 cm per sheet.

Therefore, the predicted thickness of each sheet is approximately 0.016 when rounded to three decimal places.

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