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Chapter 1: Problem 28

What is the number of significant figures in each of these measured quantities? (a) \(40.2 \mathrm{~g} / \mathrm{cm}^{3}\), (b) \(0.0000003 \mathrm{~cm}\) (c) \(70 \mathrm{~min}\) (d) \(4.6 \times 10^{19}\) atoms.

Short Answer

Expert verified
The respective number of significant figures for (a), (b), (c), and (d) are 3, 1, 1, and 2.

Step by step solution

01

Identify Significant Figures in (a) \(40.2 \mathrm{~g} / \mathrm{cm}^{3}\)

All non-zero digits are always significant. Thus, all the digits in \(40.2\) are significant. Hence, for (a) we get 3 significant figures.
02

Identify Significant Figures in (b) \(0.0000003 \mathrm{~cm}\)

Any zeroes preceding (in front of) all non-zero digits are not significant. They are present to show the decimal place. Therefore, in \(0.0000003\), only the digit \(3\) is significant. Hence, for (b) we get 1 significant figure.
03

Identify Significant Figures in (c) \(70 \mathrm{~min}\)

Here, number \(70\) could be tricky, as zeroes at the end of a number without a decimal are ambiguous - they can be either significant or insignificant. However, usually such zeroes are considered as insignificant unless specified otherwise. Hence, for (c) we get 1 significant figure.
04

Identify Significant Figures in (d) \(4.6 \times 10^{19}\) atoms

The digit \(4.6\) in \(4.6 \times 10^{19}\) is in scientific notation. All non-zero digits are also significant in this notation. Hence, for (d) we get 2 significant figures.

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Most popular questions from this chapter

The speed of sound in air at room temperature is about \(343 \mathrm{~m} / \mathrm{s}\). Calculate this speed in miles per hour \((\mathrm{mph})\)

A cylindrical glass tube \(12.7 \mathrm{~cm}\) in length is filled with mercury. The mass of mercury needed to fill the tube is found to be \(105.5 \mathrm{~g}\). Calculate the inner diameter of the tube. (The density of mercury \(=13.6 \mathrm{~g} / \mathrm{mL}\).)

(a) Convert the following temperatures to kelvin: (i) \(113^{\circ} \mathrm{C},\) the melting point of sulfur, (ii) \(37^{\circ} \mathrm{C}\), the normal body temperature, (iii) \(357^{\circ} \mathrm{C},\) the boiling point of mercury. (b) Convert the following temperatures to degrees Celsius: (i) \(77 \mathrm{~K}\), the boiling point of liquid nitrogen, (ii) \(4.2 \mathrm{~K},\) the boiling point of liquid helium, (iii) \(601 \mathrm{~K}\), the melting point of lead.

Express the answers to these in scientific notation: (a) \(145.75+\left(2.3 \times 10^{-1}\right)\) (b) \(79,500 \div\left(2.5 \times 10^{2}\right)\) (c) \(\left(7.0 \times 10^{-3}\right)-\left(8.0 \times 10^{-4}\right)\) (d) \(\left(1.0 \times 10^{4}\right) \times\left(9.9 \times 10^{6}\right)\)

Carry out these conversions: (a) 242 lb to milligrams, (b) \(68.3 \mathrm{~cm}^{3}\) to cubic meters.
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