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Chapter 1: Problem 42

Perform the following mathematical operations, and express the result to the correct number of significant figures. a. \(6.022 \times 10^{23} \times 1.05 \times 10^{2}\) b. $\frac{6.6262 \times 10^{-34} \times 2.998 \times 10^{8}}{2.54 \times 10^{-9}}$ c. \(1.285 \times 10^{-2}+1.24 \times 10^{-3}+1.879 \times 10^{-1}\) d. \(\frac{(1.00866-1.00728)}{6.02205 \times 10^{23}}\) e. $\frac{9.875 \times 10^{2}-9.795 \times 10^{2}}{9.875 \times 10^{2}} \times 100(100 \text { is exact) }$ f. $\frac{9.42 \times 10^{2}+8.234 \times 10^{2}+1.625 \times 10^{3}}{3}(3 \text { is exact) }$

Short Answer

Expert verified
a. \(6.32 \times 10^{25}\) b. \(7.826 \times 10^{-25}\) c. \(2.09 \times 10^{-1}\) d. \(2.300 \times 10^{-27}\) e. \(8.11\%\) f. \(9.79 \times 10^2\)

Step by step solution

01

Perform the multiplication using given values

To solve this problem, multiply the given values: \(6.022 \times 10^{23} \times 1.05 \times 10^{2}\)
02

Apply scientific notation rules and round the result

Multiply the values and apply the rules of scientific notation. Then round the result to the correct number of significant figures, which is three in this case: \(6.32 \times 10^{25}\) #b. Division#
03

Perform the division using given values

To solve this problem, divide the given values: \(\frac{6.6262 \times 10^{-34} \times 2.998 \times 10^{8}}{2.54 \times 10^{-9}}\)
04

Apply scientific notation rules and round the result

Divide the values, apply the rules of scientific notation, and round the result to the correct number of significant figures, which is four in this case: \(7.826 \times 10^{-25}\) #c. Addition#
05

Perform the addition using given values

To solve this problem, add the given values together: \(1.285 \times 10^{-2}+1.24 \times 10^{-3}+1.879 \times 10^{-1}\)
06

Align common exponents and round the result

Align the numbers by their common exponent, then add them and round the result to the correct number of significant figures, which is three in this case: \(2.09 \times 10^{-1}\) #d. Division#
07

Perform the division using given values

To solve this problem, divide the given values: \(\frac{(1.00866-1.00728)}{6.02205 \times 10^{23}}\)
08

Apply scientific notation rules and round the result

Perform the subtraction and division, and then round the result to the correct number of significant figures, which is four in this case: \(2.300 \times 10^{-27}\) #e. Division and Multiplication#
09

Perform the calculations using given values

To solve this problem, perform the calculations as given: \(\frac{9.875 \times 10^{2}-9.795 \times 10^{2}}{9.875 \times 10^{2}} \times 100\)
10

Apply scientific notation rules and round the result

Perform the subtraction, division, and multiplication, and then round the result to the correct number of significant figures, which is three in this case: \(8.11\%\) #f. Division and Addition#
11

Perform the calculations using given values

To solve this problem, perform the calculations as given: \(\frac{9.42 \times 10^{2}+8.234 \times 10^{2}+1.625 \times 10^{3}}{3}\)
12

Apply scientific notation rules and round the result

Perform the addition and division, and then round the result to the correct number of significant figures, which is three in this case: \(9.79 \times 10^2\)

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Most popular questions from this chapter

The density of pure silver is 10.5 \(\mathrm{g} / \mathrm{cm}^{3}\) at \(20^{\circ} \mathrm{C} .\) If 5.25 \(\mathrm{g}\) of pure silver pellets is added to a graduated cylinder containing 11.2 \(\mathrm{mL}\) of water, to what volume level will the water in the cylinder rise?

At the Amundsen-Scott South Pole base station in Antarctica, when the temperature is \(-100.0^{\circ} \mathrm{F}\) , researchers who live there can join the 4300 \(\mathrm{Club}^{\prime \prime}\) by stepping into a sauna heated to \(200.0^{\circ} \mathrm{F}\) then quickly running outside and around the pole that marks the South Pole. What are these temperatures in $^{\circ} \mathrm{C} ?\( What are these temperatures in \)\mathrm{K}$ ? If you measured the temperatures only in \(^{\circ} \mathrm{C}\) and \(\mathrm{K}\) , can you become a member of the \(" 300 \mathrm{Club}^{\prime \prime}\) (that is, is there a 300 .-degree difference between the temperature extremes when measured in \(^{\circ} \mathrm{C}\) and \(\mathrm{K}\) )?

Which of the following describes a chemical property? a. The density of iron is 7.87 \(\mathrm{g} / \mathrm{cm}^{3} .\) b. A platinum wire glows red when heated. c. An iron bar rusts. d. Aluminum is a silver-colored metal.

Diamonds are measured in carats, and 1 carat \(=0.200 \mathrm{g} .\) The density of diamond is 3.51 \(\mathrm{g} / \mathrm{cm}^{3}\) . a. What is the volume of a 5.0 -carat diamond? b. What is the mass in carats of a diamond measuring 2.8 \(\mathrm{mL} ?\)

At what temperature is the temperature in degrees Fahrenheit equal to twice the temperature in degrees Celsius?
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