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Chapter 1: Problem 39

Evaluate each of the following, and write the answer to the appropriate number of significant figures. a. \(212.2+26.7+402.09\) b. \(1.0028+0.221+0.10337\) c. \(52.331+26.01-0.9981\) d. \(2.01 \times 10^{2}+3.014 \times 10^{3}\) e. \(7.255-6.8350\)

Short Answer

Expert verified
a. Answer: 641.1 b. Answer: 1.327 c. Answer: 77.34 d. Answer: 3215 e. Answer: 0.42

Step by step solution

01

Add the numbers

Add the given numbers: \(212.2+26.7+402.09 = 641.09\)
02

Determine the appropriate number of significant figures

In addition and subtraction, we look at the least number of decimal places in the given numbers. In this case, they are 1, 1, and 2, respectively. The least number of decimal places is 1. Therefore, the answer should have only one decimal place.
03

Round the result to the appropriate number of significant figures

Round the result to one decimal place: \(641.09\) becomes \(641.1\) #a. Answer: 641.1# #b. 1.0028+0.221+0.10337#
04

Add the numbers

Add the given numbers: \(1.0028+0.221+0.10337 = 1.32717\)
05

Determine the appropriate number of significant figures

In this case, the least number of decimal places is 3, so the answer should havethree decimal places.
06

Round the result to the appropriate number of significant figures

Round the result to three decimal places: \(1.32717\) becomes \(1.327\) #b. Answer: 1.327# #c. 52.331+26.01-0.9981#
07

Add and subtract the numbers

Calculate the expression: \(52.331 + 26.01 - 0.9981 = 77.3429\)
08

Determine the appropriate number of significant figures

In this case, the least number of decimal places is 2. So, the answer should have two decimal places.
09

Round the result to the appropriate number of significant figures

Round the result to two decimal places: \(77.3429\) becomes \(77.34\) #c. Answer: 77.34# #d. 2.01 * 10^{2} + 3.014 * 10^{3}#
10

Convert to standard notation

Convert the given scientific notation expressions to standard notation: \(201 + 3014 = 3215\)
11

Determine the appropriate number of significant figures

In this problem, the original numbers of significant figures in the given numbers were 3 and 4, respectively. Therefore, the answer should have the least number of significant figures, which is 3.
12

Round the result to the appropriate number of significant figures

Round the result to three significant figures: \(3215\) remains the same - \(3215\) #d. Answer: 3215# #e. 7.255-6.8350#
13

Subtract the numbers

Subtract the given numbers: \(7.255 - 6.8350 = 0.42\)
14

Determine the appropriate number of significant figures

In this case, the least number of decimal places is 2. So, the answer should have two decimal places.
15

Round the result to the appropriate number of significant figures

Round the result to two decimal places: \(0.42\) remains the same - \(0.42\) #e. Answer: 0.42#

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Most popular questions from this chapter

Convert the following Celsius temperatures to Kelvin and to Fahrenheit degrees. a. the temperature of someone with a fever, \(39.2^{\circ} \mathrm{C}\) b. a cold wintery day, \(-25^{\circ} \mathrm{C}\) c. the lowest possible temperature, \(-273^{\circ} \mathrm{C}\) d. the melting-point temperature of sodium chloride, \(801^{\circ} \mathrm{C}\)

Convert the following Fahrenheit temperatures to the Celsius and Kelvin scales. a. \(-459^{\circ} \mathrm{F}\) , an extremely low temperature b. \(-40 .^{\circ} \mathrm{F}\) , the answer to a trivia question c. \(68^{\circ} \mathrm{F}\) , room temperature d. \(7 \times 10^{7}\) F, temperature required to initiate fusion reactions in the sun

Is the density of a gaseous substance larger or smaller than the density of a liquid or a solid at the same temperature? Why?

The U.S. trade deficit at the beginning of 2005 was \(\$ 475,000,000\) . If the wealthiest 1.00\(\%\) of the U.S. population \((297,000,000)\) contributed an equal amount of money to bring the trade deficit to \(\$ 0,\) how many dollars would each person contribute? If one of these people were to pay his or her share in nickels only, how many nickels are needed? Another person contribute? If one of these people were to pay his or her share in nickels only, how many nickels are needed? Another person living abroad at the time decides to pay in pounds sterling (f). How many pounds sterling does this person contribute (assume a conversion rate of \(1 \mathrm{f}=\$ 1.869\) )?

You have two beakers, one filled to the 100-mL mark with sugar (the sugar has a mass of 180.0 g) and the other filled to the 100-mL mark with water (the water has a mass of 100.0 g). You pour all the sugar and all the water together in a bigger beaker and stir until the sugar is completely dissolved. a. Which of the following is true about the mass of the solution? Explain. i. It is much greater than 280.0 g. ii. It is somewhat greater than 280.0 g. iii. It is exactly 280.0 g. iv. It is somewhat less than 280.0 g. v. It is much less than 280.0 g. b. Which of the following is true about the volume of the solution? Explain. i. It is much greater than 200.0 mL. ii. It is somewhat greater than 200.0 mL. iii. It is exactly 200.0 mL. iv. It is somewhat less than 200.0 mL. v. It is much less than 200.0 mL.
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