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Chapter 1: Problem 33

Express the answers to the following calculations in scientific notation: (a) \(145.75+\left(2.3 \times 10^{-1}\right)\) (b) \(79,500 \div\left(2.5 \times 10^{2}\right)\) (c) \(\left(7.0 \times 10^{-3}\right)-\left(8.0 \times 10^{-4}\right)\) (d) \(\left(1.0 \times 10^{4}\right) \times\left(9.9 \times 10^{6}\right)\)

Short Answer

Expert verified
(a) \(1.4805 \times 10^{2}\), (b) \(3.18 \times 10^{2}\), (c) \(6.2 \times 10^{-3}\), (d) \(9.9 \times 10^{10}\)

Step by step solution

01

Addition

(a) To perform the operation \(145.75+(2.3 \times 10^{-1})\), first convert \(145.75\) into scientific notation, obtaining \(1.4575 \times 10^{2}\). Then, add \(1.4575 \times 10^{2}\) to \(2.3 \times 10^{-1}\) by bringing them to the common exponent, here \(10^{2}\). We get \(1.4575 \times 10^{2} + 0.023 \times 10^{2} = 1.4805 \times 10^{2}\).
02

Division

(b) In the equation \(79500 \div(2.5 \times 10^{2})\), first, express \(79500\) in scientific notation as \(7.95 \times 10^{4}\). Then, divide \(7.95 \times 10^{4}\) by \(2.5 \times 10^{2}\). This yields \(7.95 \times 10^{4-2} \div 2.5 = 3.18 \times 10^{2}\).
03

Subtraction

(c) In order to subtract \((7.0 \times 10^{-3})-(8.0 \times 10^{-4})\), bring them to a common exponent, here \(10^{-3}\). We get \(7.0 \times 10^{-3} - 0.8 \times 10^{-3} = 6.2 \times 10^{-3}\).
04

Multiplication

(d) The multiplication operation \((1.0 \times 10^{4}) \times (9.9 \times 10^{6})\) simplifies by multiplying the numbers and adding the exponents to get \(1.0 \times 9.9 \times 10^{4+6} = 9.9 \times 10^{10}\).

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Most popular questions from this chapter

Carry out the following operations as if they were calculations of experimental results, and express each answer in the correct units with the correct number of significant figures: (a) \(5.6792 \mathrm{~m}+0.6 \mathrm{~m}+4.33 \mathrm{~m}\) (b) \(3.70 \mathrm{~g}-2.9133 \mathrm{~g}\) (c) \(4.51 \mathrm{~cm} \times 3.6666 \mathrm{~cm}\) (d) \(\left(3 \times 10^{4} \mathrm{~g}+6.827 \mathrm{~g}\right) /\left(0.043 \mathrm{~cm}^{3}-0.021 \mathrm{~cm}^{3}\right)\)

A sheet of aluminum (AI) foil has a total area of \(1.000 \mathrm{ft}^{2}\) and a mass of \(3.636 \mathrm{~g}\). What is the thickness of the foil in millimeters? (Density of Al = \(\left.2.699 \mathrm{~g} / \mathrm{cm}^{3} .\right)\)

Which of the following statements describe physical properties and which describe chemical properties? (a) Iron has a tendency to rust. (b) Rainwater in industrialized regions tends to be acidic. (c) Hemoglobin molecules have a red color. (d) When a glass of water is left out in the sun, the water gradually disappears. (e) Carbon dioxide in air is converted to more complex molecules by plants during photosynthesis.

Chlorine is used to disinfect swimming pools. The accepted concentration for this purpose is 1 ppm chlorine, or \(1 \mathrm{~g}\) of chlorine per million grams of water. Calculate the volume of a chlorine solution (in milliliters) a homeowner should add to her swimming pool if the solution contains 6.0 percent chlorine by mass and there are \(2.0 \times 10^{4}\) gallons of water in the pool. ( 1 gallon \(=3.79 \mathrm{~L} ;\) density of liquids $=1.0 \mathrm{~g} / \mathrm{mL} .

At what temperature does the numerical reading on a Celsius thermometer equal that on a Fahrenheit thermometer?
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