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Chapter 2: Problem 85

Convert each length to meters. Report your answers in scientific notation and watch your significant figures. (a) \(2.31\) gigameters \((\mathrm{Gm})\) (b) \(5.00\) micrometers \((\mu m)\) (c) 1004 millimeters \((\mathrm{mm})\) (d) \(5.00\) picometers \((\mathrm{pm})\) (e) \(0.25\) kilometer \((\mathrm{km})\)

Short Answer

Expert verified
(a) \(2.31 \times 10^9\) m (b) \(5.00 \times 10^{-6}\) m (c) \(1.004 \times 10^{0}\) m (d) \(5.00 \times 10^{-12}\) m (e) \(2.5 \times 10^{2}\) m

Step by step solution

01

1. Converting gigameters (Gm) to meters (m)

To convert gigameters to meters, we will multiply the given length (in gigameters) by the conversion factor: 1 Gm = \(10^9\) m. So, for 2.31 Gm, we have: \(2.31\,\mathrm{Gm} \times 10^9\,\mathrm{m/Gm}\) Now, multiply the numbers: \(2.31 \times 10^9\) m which is already in scientific notation and has the correct number of significant figures.
02

2. Converting micrometers (µm) to meters (m)

To convert micrometers to meters, we will multiply the given length (in micrometers) by the conversion factor: 1 µm = \(10^{-6}\) m. So, for 5.00 µm, we have: \(5.00\,\mathrm{µm} \times 10^{-6}\,\mathrm{m/µm}\) Now, multiply the numbers: \(5.00 \times 10^{-6}\) m which is already in scientific notation and has the correct number of significant figures.
03

3. Converting millimeters (mm) to meters (m)

To convert millimeters to meters, we will multiply the given length (in millimeters) by the conversion factor: 1 mm = \(10^{-3}\) m. So, for 1004 mm, we have: \(1004\,\mathrm{mm} \times 10^{-3}\,\mathrm{m/mm}\) Now, multiply the numbers: \(1.004 \times 10^{3}\) m \(\times 10^{-3}\,\mathrm{m/mm}\) When simplified, we get: \(1.004 \times 10^{0}\) m, which is already in scientific notation and has the correct number of significant figures.
04

4. Converting picometers (pm) to meters (m)

To convert picometers to meters, we will multiply the given length (in picometers) by the conversion factor: 1 pm = \(10^{-12}\) m. So, for 5.00 pm, we have: \(5.00\,\mathrm{pm} \times 10^{-12}\,\mathrm{m/pm}\) Now, multiply the numbers: \(5.00 \times 10^{-12}\) m is already in scientific notation and has the correct number of significant figures.
05

5. Converting kilometers (km) to meters (m)

To convert kilometers to meters, we will multiply the given length (in kilometers) by the conversion factor: 1 km = \(10^{3}\) m. So, for 0.25 km, we have: \(0.25\,\mathrm{km} \times 10^{3}\,\mathrm{m/km}\) Now, multiply the numbers: \(2.5 \times 10^{-1}\) m \(\times 10^{3}\,\mathrm{m/km}\) When simplified, we get: \(2.5 \times 10^{2}\) m, which is in scientific notation and has the correct number of significant figures.

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Most popular questions from this chapter

On a hot summer day, you want to cool two glasses of warm lemonade, but have no ice. Not wanting to wait until you can make some, you place two small metal blocks in the freezer. One block is pure iron, the other pure aluminum, and each has a mass of exactly \(50 \mathrm{~g}\). After both have cooled to \(-10^{\circ} \mathrm{C}\), you put them into separate glasses and add \(200 \mathrm{~mL}\) of warm lemonade to each. After a few minutes, both blocks have warmed up to \(+10{ }^{\circ} \mathrm{C}\). At this point, is the lemonade in one glass cooler than the lemonade in the other glass? If so, which is cooler and why? (Despite all the numerical information, you should be able to use specific heat values from Table \(2.5\) to answer without doing any calculations.)

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