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Chapter 1: Problem 24

Use appropriate metric prefixes to write the following measurements without use of exponents: (a) \(2.3 \times 10^{-10} \mathrm{~L}\) (b) \(4.7 \times 10^{-6} \mathrm{~g}\), (c) \(1.85 \times 10^{-12} \mathrm{~m}\) (d) \(16.7 \times 10^{6} \mathrm{~s}\); (e) \(15.7 \times 10^{3} \mathrm{~g}\) (f) \(1.34 \times 10^{-3} \mathrm{~m},(\mathrm{~g}) 1.84 \times 10^{2} \mathrm{~cm}\)

Short Answer

Expert verified
(a) 230 pL (b) 4.7 µg (c) 1.85 pm (d) 16.7 Ms (e) 15.7 kg (f) 1.34 mm, 1.84 m

Step by step solution

01

Finding SI prefix for (a)

For (a), we have \(2.3 \times 10^{-10} L\). The exponent is -10, which corresponds to the SI prefix "pico" (p, \(10^{-12}\)). Therefore, we can rewrite this as 230 pL.
02

Finding SI prefix for (b)

For (b), we have \(4.7 \times 10^{-6} g\). The exponent is -6, which corresponds to the SI prefix "micro" (µ, \(10^{-6}\)). Therefore, we can rewrite this as 4.7 µg.
03

Finding SI prefix for (c)

For (c), we have \(1.85 \times 10^{-12} m\). The exponent is -12, which corresponds to the SI prefix "pico" (p, \(10^{-12}\)). Therefore, we can rewrite this as 1.85 pm.
04

Finding SI prefix for (d)

For (d), we have \(16.7 \times 10^{6} s\). The exponent is 6, which corresponds to the SI prefix "mega" (M, \(10^6\)). Therefore, we can rewrite this as 16.7 Ms.
05

Finding SI prefix for (e)

For (e), we have \(15.7 \times 10^{3} g\). The exponent is 3, which corresponds to the SI prefix "kilo" (k, \(10^3\)). Therefore, we can rewrite this as 15.7 kg.
06

Finding SI prefix for (f)

For (f), we have two quantities: \(1.34 \times 10^{-3} m\) and \(1.84 \times 10^{2} cm\). For the first quantity, the exponent is -3, which corresponds to the SI prefix "milli" (m, \(10^{-3}\)). Therefore, we can rewrite this as 1.34 mm. For the second quantity, note the unit is cm, and the exponent is 2, which corresponds to the SI prefix "hecto" (h, \(10^2\)). To stay in the base unit of meters, we convert 1 cm in meters first, which is equal to \(1 \times 10^{-2} m\). Then, we can rewrite this as \( 1.84 \times 10^{2} \times 10^{-2} m = 1.84 m\). Final answers: (a) 230 pL (b) 4.7 µg (c) 1.85 pm (d) 16.7 Ms (e) 15.7 kg (f) 1.34 mm, 1.84 m

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Most popular questions from this chapter

Water has a density of \(0.997 \mathrm{~g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C} ;\) ice has a density of \(0.917 \mathrm{~g} / \mathrm{cm}^{3}\) at \(-10^{\circ} \mathrm{C}\). (a) If a soft-drink bottle whose volume is \(1.50 \mathrm{~L}\) is completely filled with water and then frozen to \(-10^{\circ} \mathrm{C},\) what volume does the ice occupy? (b) Can the ice be contained within the bottle?

Silicon for computer chips is grown in large cylinders called "boules" that are \(300 \mathrm{~mm}\) in diameter and \(2 \mathrm{~m}\) in height. The density of silicon is \(2.33 \mathrm{~g} / \mathrm{cm}^{3}\). Silicon wafers for making integrated circuits are sliced from a \(2.0 \mathrm{~m}\) boule and are typically \(0.75 \mathrm{~mm}\) thick and \(300 \mathrm{~mm}\) in diameter. (a) How many wafers can be cut from a single boule? (b) What is the mass of a silicon wafer? (The volume of a cylinder is given by \(\pi r^{2} h\), where \(r\) is the radius and \(h\) is its height.)

Automobile batteries contain sulfuric acid, which is commonly referred to as "battery acid." Calculate the number of grams of sulfuric acid in 1.00 gallon of battery acid if the solution has a density of \(1.28 \mathrm{~g} / \mathrm{mL}\) and is \(38.1 \%\) sulfuric acid by mass.

Round each of the following numbers to four significant figures, and express the result in standard exponential notation: (c) \(0.008543210,\) (d) 0.000257870 , (a) \(102.53070,(\mathbf{b}) 656,980,\) (e) -0.0357202 .

In the process of attempting to characterize a substance, a chemist makes the following observations: The substance is a silvery white, lustrous metal. It melts at \(649^{\circ} \mathrm{C}\) and boils at \(1105^{\circ} \mathrm{C}\). Its density at \(20{ }^{\circ} \mathrm{C}\) is \(1.738 \mathrm{~g} / \mathrm{cm}^{3}\). The substance burns in air, producing an intense white light. It reacts with chlorine to give a brittle white solid. The substance can be pounded into thin sheets or drawn into wires. It is a good conductor of electricity. Which of these characteristics are physical properties, and which are chemical properties?
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