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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

Expert verified
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

The unit of land measure in the English system is the acre, while that in the metric system is the hectare. An acre is \(4.356 \times 10^{4} \mathrm{ft}^{2} .\) A hectare is ten thousand square meters. The town of Willington in Connecticut requires a minimum area of \(2.0\) acres of land for a single-family dwelling. How many hectares are required?

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.)

Potassium sulfate has a solubility of \(15 \mathrm{~g} / 100 \mathrm{~g}\) water at \(40^{\circ} \mathrm{C}\). A solution is prepared by adding \(39.0 \mathrm{~g}\) of potassium sulfate to \(225 \mathrm{~g}\) of water, carefully heating the solution, and cooling it to \(40^{\circ} \mathrm{C}\). A homogeneous solution is obtained. Is this solution saturated, unsaturated, or supersaturated? The beaker is shaken, and precipitation occurs. How many grams of potassium sulfate would you expect to crystallize out?

The solubility of lead nitrate at \(100^{\circ} \mathrm{C}\) is \(140.0 \mathrm{~g} / 100 \mathrm{~g}\) water. A solution at \(100^{\circ} \mathrm{C}\) consists of \(57.0 \mathrm{~g}\) of lead nitrate in \(64.0 \mathrm{~g}\) of water. When the solution is cooled to \(10^{\circ} \mathrm{C}, 25.0 \mathrm{~g}\) of lead nitrate crystallize out. What is the solubility of lead nitrate in \(g / 100 \mathrm{~g}\) water at \(10^{\circ} \mathrm{C} ?\)

How would you separate into its different components (a) a mixture of the volatile gases propane, butane, and isopropane? (b) a solution of rubbing alcohol made up of isopropyl alcohol and water?
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