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Chapter 1: Problem 43

Indicate which of the following are exact numbers: (a) the mass of a 7.5 - by \(12.5-\mathrm{cm}\) index card, \((\mathbf{b})\) the number of grams in a kilogram, \((\mathbf{c})\) the volume of a cup of Seattle's Best coffee, (d) the number of centimeters in a kilometer, \((\mathbf{e})\) the number of microseconds in a week, \((\mathbf{f})\) the number of pages in this book.

Short Answer

Expert verified
The exact numbers from the given list are: (b) the number of grams in a kilogram, (d) the number of centimeters in a kilometer, and (e) the number of microseconds in a week. The other quantities are not exact numbers due to factors like material, size, and uncertainty.

Step by step solution

01

(a) Mass of a 7.5 x 12.5 cm index card

The mass of a 7.5 x 12.5 cm index card cannot be an exact number as it depends on the material of the card and can vary between different cards of the same size. So, this is not an exact number.
02

(b) Number of grams in a kilogram

By definition, there are exactly 1000 grams in a kilogram. Thus, this is an exact number.
03

(c) Volume of a cup of Seattle's Best coffee

The volume of a cup of Seattle's Best coffee is not an exact number because it depends on the size of the cup used and other factors such as how much coffee is poured. Therefore, this is not an exact number.
04

(d) Number of centimeters in a kilometer

By definition, there are exactly 100,000 centimeters in a kilometer (1 kilometer = 1000 meters, 1 meter = 100 centimeters). Thus, this is an exact number.
05

(e) Number of microseconds in a week

A week has a fixed duration of 7 days, where each day has 24 hours, each hour has 60 minutes, each minute has 60 seconds, and each second has 1,000,000 microseconds. So, we can calculate the exact number of microseconds in a week as follows: \(7 \times 24 \times 60 \times 60 \times 1,000,000 = 604,800,000,000\) microseconds. This is an exact number.
06

(f) Number of pages in this book

The number of pages in a book is an exact number, as it refers to a specific, countable quantity. However, since we don't have the information about the book in question, we can't provide the actual numerical value. Nonetheless, this would be considered an exact number.

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Most popular questions from this chapter

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convert (a) in. to \(\mathrm{cm}(\mathbf{b}) \mathrm{lb}\) to \(\mathrm{g}\) (c) \(\mu g\) to \(g\) (d) \(\mathrm{ft}^{2}\) to \(\mathrm{cm}^{2}\).

A \(30.0-\mathrm{cm}\) -long cylindrical plastic tube, sealed at one end, is filled with acetic acid. The mass of acetic acid needed to fill the tube is found to be \(89.24 \mathrm{~g}\). The density of acetic acid is $1.05 \mathrm{~g} / \mathrm{mL}$. Calculate the inner diameter of the tube in centimeters.

Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is \(22.52 \%\). The students' results for three determinations are as follows: (1) 22.52,22.48,22.54 (2) 22.64,22.58,22.62 (a) Calculate the average percentage for each set of data and state which set is the more accurate based on the average. (b) Precision can be judged by examining the average of the deviations from the average value for that data set. (Calculate the average value for each data set; then calculate the average value of the absolute deviations of each measurement from the average.) Which set is more precise?

A \(10.0 \mathrm{~g}\) block of gold is hammered into a thin gold sheet which has an area of \(150 \mathrm{~cm}^{2}\). Given the density of gold is $19.3 \mathrm{~g} / \mathrm{cm}^{3}$, what is the approximate thickness of the gold sheet in millimeters?

Round each of the following numbers to three significant figures and express the result in standard exponential notation: $(\mathbf{a}) 2048732.23(\mathbf{b}) 0.000292945(\mathbf{c})-82454.09$ (d) \(942.057024(\mathbf{e})-0.00000324683 .\)
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