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Chapter 1: Problem 17

How many significant figures are there in each of the following? (a) \(12.7040 \mathrm{~g}\) (b) \(200.0 \mathrm{~cm}\) (c) \(276.2\) tons (d) \(4.00 \times 10^{3} \mathrm{~mL}\) (e) \(100^{\circ} \mathrm{C}\)

Short Answer

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Question: Determine the number of significant figures in each of the following values: (a) \(12.7040 \mathrm{~g}\) (b) \(200.0 \mathrm{~cm}\) (c) \(276.2\) tons (d) \(4.00 \times 10^{3} \mathrm{~mL}\) (e) \(100^{\circ} \mathrm{C}\) Answer: (a) 6 significant figures (b) 4 significant figures (c) 4 significant figures (d) 3 significant figures (e) 1 significant figure

Step by step solution

01

(a) Counting significant figures in \(12.7040 \mathrm{~g}\)#

Start counting from the first non-zero digit on the left and move to the right till the last digit, including any zeros in between or at the end. In this case, there are 6 significant figures: \(1, 2, 7, 0, 4, 0\).
02

(b) Counting significant figures in \(200.0 \mathrm{~cm}\)#

Start counting from the first non-zero digit on the left and move to the right till the last digit, including any zeros in between or at the end. In this case, there are 4 significant figures: \(2, 0, 0, 0\). The last trailing zero is also included, as it's after the decimal point.
03

(c) Counting significant figures in \(276.2\) tons#

Start counting from the first non-zero digit on the left and move to the right till the last digit, including any zeros in between. In this case, there are 4 significant figures: \(2, 7, 6, 2\).
04

(d) Counting significant figures in \(4.00 \times 10^{3} \mathrm{~mL}\)#

In scientific notation, we only need to count the significant figures in the number preceding the exponent. In this case, there are 3 significant figures: \(4, 0, 0\). The zeros after the decimal point are significant.
05

(e) Counting significant figures in \(100^{\circ} \mathrm{C}\)#

Start counting from the first non-zero digit on the left and move to the right. In this case, there are 1 significant figure: \(1\). The other zeros are considered as placeholders and do not count as significant figures as there is no decimal point.

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Most popular questions from this chapter

Ammonium bromide can be used as a wood preservative. Its solubility in water at \(20^{\circ} \mathrm{C}\) is \(75.5 \mathrm{~g} / 100 \mathrm{~g}\) water. At \(50^{\circ} \mathrm{C}\) its solubility is \(99.2 \mathrm{~g} / 100 \mathrm{~g}\) water. Calculate (a) the mass of ammonium bromide that dissolves in \(82.5 \mathrm{~g}\) of water at \(20^{\circ} \mathrm{C} .\) (b) the mass of water required to dissolve \(43.7 \mathrm{~g}\) of ammonium bromide at \(50^{\circ} \mathrm{C}\). (c) the mass of ammonium bromide that would not remain in solu- tion if a solution made up of \(29.0 \mathrm{~g}\) of ammonium bromide in \(35.0 \mathrm{~g}\) of water at \(50^{\circ} \mathrm{C}\) is cooled to \(20^{\circ} \mathrm{C}\).

An average adult breathes about \(8.50 \times 10^{3} \mathrm{~L}\) of air per day. The concentration of lead in highly polluted urban air is \(7.0 \times 10^{-6} \mathrm{~g}\) of lead per one \(\mathrm{m}^{3}\) of air. Assume that \(75 \%\) of the lead is present as particles less than \(1.0 \times 10^{-6} \mathrm{~m}\) in diameter, and that \(50 \%\) of the particles below that size are retained in the lungs. Calculate the mass of lead absorbed in this manner in 1 year by an average adult living in this environment.

Calculate the following to the correct number of significant figures. Assume that all these numbers are measurements. (a) \(x=17.2+65.18-2.4\) (b) \(x=\frac{13.0217}{17.10}\) (c) \(x=(0.0061020)(2.0092)(1200.00)\) (d) \(x=0.0034+\frac{\sqrt{(0.0034)^{2}+4(1.000)\left(6.3 \times 10^{-4}\right)}}{(2)(1.000)}\)

A listing of a house for sale states that there are 5 bedrooms, \(4000 \mathrm{ft}^{2}\) of living area, and a living room with dimensions \(17 \times 18.5 \mathrm{ft}\). How many significant figures are there in each quantity? (Your answer may include the words ambiguous and exact.)

The Kohinoor Diamond \(\left(d=3.51 \mathrm{~g} / \mathrm{cm}^{3}\right)\) is 108 carats. If one carat has a mass of \(2.00 \times 10^{2} \mathrm{mg}\), what is the mass of the Kohinoor Diamond in pounds? What is the volume of the diamond in cubic inches?
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