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Chapter 1: Problem 36

Perform the following mathematical operations, and express each result to the correct number of significant figures. a. \(\frac{0.102 \times 0.0821 \times 273}{1.01}\) b. \(0.14 \times 6.022 \times 10^{23}\) c. \(4.0 \times 10^{4} \times 5.021 \times 10^{-3} \times 7.34993 \times 10^{2}\) d. \(\frac{2.00 \times 10^{6}}{3.00 \times 10^{-7}}\)

Short Answer

Expert verified
The short answers for the given mathematical operations are: a. \(2.22\) b. \(8.4 \times 10^{22}\) c. \(1.5 \times 10^{4}\) d. \(6.67 \times 10^{12}\)

Step by step solution

01

Make sure the numbers have the correct number of significant figures

First, identify the given numbers: \(0.102\) has 3 significant figures, \(0.0821\) has 4 significant figures, \(273\) has 3 significant figures, and \(1.01\) has 3 significant figures.
02

Perform the calculation

Multiply the numbers in the numerator and divide by the denominator, keeping track of the least number of significant figures: \(\frac{0.102 \times 0.0821 \times 273}{1.01} \approx 2.22\) Since the least number of significant figures is 3, the result has 3 significant figures: \(2.22\). #b. Calculate \(0.14 \times 6.022 \times 10^{23}\)#
03

Make sure the numbers have the correct number of significant figures

First, identify the given numbers: \(0.14\) has 2 significant figures, and \(6.022 \times 10^{23}\) has 4 significant figures.
04

Perform the calculation

Multiply the given numbers, keeping the least number of significant figures: \(0.14 \times 6.022 \times 10^{23} \approx 8.4 \times 10^{22}\) Since the least number of significant figures is 2, the result has 2 significant figures: \(8.4 \times 10^{22}\). #c. Calculate \(4.0 \times 10^{4} \times 5.021 \times 10^{-3} \times 7.34993 \times 10^{2}\)#
05

Make sure the numbers have the correct number of significant figures

First, identify the given numbers: \(4.0 \times 10^{4}\) has 2 significant figures, \(5.021 \times 10^{-3}\) has 4 significant figures, and \(7.34993 \times 10^{2}\) has 6 significant figures.
06

Perform the calculation

Multiply the given numbers, keeping the least number of significant figures: \(4.0 \times 10^{4} \times 5.021 \times 10^{-3} \times 7.34993 \times 10^{2} \approx 1.5 \times 10^{4}\) Since the least number of significant figures is 2, the result has 2 significant figures: \(1.5 \times 10^{4}\). #d. Calculate \(\frac{2.00 \times 10^{6}}{3.00 \times 10^{-7}}\)#
07

Make sure the numbers have the correct number of significant figures

First, identify the given numbers: \(2.00 \times 10^{6}\) has 3 significant figures, and \(3.00 \times 10^{-7}\) has 3 significant figures.
08

Perform the calculation

Divide the numbers, keeping the least number of significant figures: \(\frac{2.00 \times 10^{6}}{3.00 \times 10^{-7}} \approx 6.67 \times 10^{12}\) Since both numbers have 3 significant figures, the result also has 3 significant figures: \(6.67 \times 10^{12}\).

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Most popular questions from this chapter

Lipitor, a pharmaceutical drug that has been shown to lower "bad" cholesterol levels while raising "good" cholesterol levels in patients taking the drug, had over \(\$ 11\) billion in sales in 2006 . Assuming one \(2.5\) -g pill contains \(4.0 \%\) of the active ingredient by mass, what mass in \(\mathrm{kg}\) of active ingredient is present in one bottle of 100 . pills?

Many times errors are expressed in terms of percentage. The percent error is the absolute value of the difference of the true value and the experimental value, divided by the true value, and multiplied by 100 . Percent error \(=\frac{\mid \text { true value }-\text { experimental value } \mid}{\text { true value }} \times 100\) Calculate the percent error for the following measurements. a. The density of an aluminum block determined in an experiment was \(2.64 \mathrm{~g} / \mathrm{cm}^{3}\). (True value \(2.70 \mathrm{~g} / \mathrm{cm}^{3}\).) b. The experimental determination of iron in iron ore was \(16.48 \%\). (True value \(16.12 \% .)\) c. A balance measured the mass of a \(1.000-\mathrm{g}\) standard as \(0.9981 \mathrm{~g}\)

When a marble is dropped into a beaker of water, it sinks to the bottom. Which of the following is the best explanation? a. The surface area of the marble is not large enough to be held up by the surface tension of the water. b. The mass of the marble is greater than that of the water. c. The marble weighs more than an equivalent volume of the water. d. The force from dropping the marble breaks the surface tension of the water. e. The marble has greater mass and volume than the water. Justify your choice, and for choices you did not pick, explain what is wrong about them.

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You are in Paris, and you want to buy some peaches for lunch. The sign in the fruit stand indicates that peaches cost \(2.45\) euros per kilogram. Given that 1 euro is equivalent to approximately \(\$ 1.46\), calculate what a pound of peaches will cost in dollars.
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