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Chapter 1: Problem 54

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convert (a) \(\mathrm{km} / \mathrm{hr}\) to \(\mathrm{m} / \mathrm{s}\) (b) \(\mathrm{mL}\) to \(\mu \mathrm{L}(\mathbf{c}) \mathrm{ps}\) to $\mathrm{s}(\mathbf{d}) \mathrm{m}^{3}$ to gal.

Short Answer

Expert verified
To convert (a) km/hr to m/s, multiply the value by \( \frac{5}{18} \). (b) To convert mL to µL, multiply the value by 1000. (c) To convert ps to s, multiply the value by \(\frac{1}{10^{12}}\). (d) To convert m³ to gal, multiply the value by 264.172.

Step by step solution

01

(a) Converting kilometers per hour to meters per second

First, we need to convert kilometers to meters as there are 1000 meters in 1 kilometer. Next, we'll need to convert hours to seconds, since there are 3600 seconds in an hour. The conversion factor for this problem can be found as follows: \[\frac{\text{1 km}}{\text{1 hr}} =\frac{1000\text{ m}}{3600\text{ s}} \Rightarrow \frac{\text{km}}{\text{hr}} = \frac{5}{18} \frac{\text{m}}{\text{s}}\] To convert a given value in km/hr to m/s, multiply it by the conversion factor (5/18).
02

(b) Converting milliliters to microliters

To perform this conversion, we need to know that there are 1000 microliters (µL) in 1 milliliter (mL). Therefore, the conversion factor for this problem is: \[\frac{\text{1 mL}}{\text{1}} =\frac{1000\text{ µL}}{\text{1}} \Rightarrow \frac{\text{mL}}{\text{1}} = \frac{\text{1000 µL}}{\text{1}}\] To convert a given value in mL to µL, multiply it by 1000.
03

(c) Converting picoseconds to seconds

To convert picoseconds (ps) to seconds (s), we need to know that 1 second equals 10^12 picoseconds. The conversion factor for this problem is: \[\frac{\text{1 s}}{10^{12}\text{ ps}} \Rightarrow \frac{\text{s}}{\text{ps}} = \frac{1}{10^{12}}\] To convert a given value in picoseconds to seconds, multiply it by the conversion factor (1/10^12).
04

(d) Converting cubic meters to gallons

To convert cubic meters (m³) to gallons (gal), we need to know the conversion factor, which is 264.172 gallons per cubic meter. The conversion factor for this problem is: \[\frac{\text{1 m}^{3}}{\text{1}} =\frac{264.172\text{ gal}}{\text{1}} \Rightarrow \frac{\text{m}^{3}}{\text{1}} = \frac{264.172\text{ gal}}{\text{1}}\] To convert a given value in cubic meters to gallons, multiply it by the conversion factor (264.172).

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Most popular questions from this chapter

Classify each of the following as a pure substance or a mixture, If a mixture, indicate whether it is homogeneous or heterogeneous: (a) milk, (b) beer, (c) diamond, (d) mayonnaise.

What is the number of significant figures in each of the following measured quantities? (a) \(902.5 \mathrm{~kg}\), (b) \(3 \times 10^{-6} \mathrm{~m}\), (c) \(0.0096 \mathrm{~L}\), (d) \(2.94 \times 10^{3} \mathrm{~m}^{2}\) (e) \(92.03 \mathrm{~km}\) (f) \(782.234 \mathrm{~g}\).

Identify each of the following as measurements of length, area, volume, mass, density, time, or temperature: (a) \(25 \mathrm{ps}\), (b) \(374.2 \mathrm{mg}\) (c) \(77 \mathrm{~K}\) (d) \(100,000 \mathrm{~km}^{2}\) (e) \(1.06 \mu \mathrm{m}\) (f) \(16 \mathrm{nm}^{2},(\mathrm{~g})-78^{\circ} \mathrm{C}\) (h) \(2.56 \mathrm{~g} / \mathrm{cm}^{3}\) (i) \(28 \mathrm{~cm}^{3}\). [Section \(\left.1.5\right]\)

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