Problem 72 - Chemistry Principles and Practice

Question

Carry out each of the following conversions: (a) \(25.5 \mathrm{~m}\) to \(\mathrm{km}\) (b) \(36.3 \mathrm{~km}\) to \(\mathrm{m}\) (c) \(487 \mathrm{~kg}\) to \(\mathrm{g}\) (d) \(1.32 \mathrm{~L}\) to \(\mathrm{mL}\) (e) \(55.9 \mathrm{dL}\) to \(\mathrm{L}\) (f) \(6251 \mathrm{~L}\) to \(\mathrm{cm}^{3}\)

Step-by-Step Solution

Answer

(a) 0.0255 km, (b) 36300 m, (c) 487000 g, (d) 1320 mL, (e) 5.59 L, (f) 6251000 cm³.

Step 1: Convert meters to kilometers

To convert from meters to kilometers, divide the number of meters by 1000. For part (a), we have 25.5 m, so divide it by 1000: \(25.5 \, \mathrm{m} \, / \, 1000 = 0.0255 \, \mathrm{km}\)

Step 2: Convert kilometers to meters

To convert from kilometers to meters, multiply the number of kilometers by 1000. For part (b), we have 36.3 km, thus multiply by 1000: \(36.3 \, \mathrm{km} \, \times \, 1000 = 36300 \, \mathrm{m}\)

Step 3: Convert kilograms to grams

To convert from kilograms to grams, multiply the number of kilograms by 1000. For part (c), we have 487 kg, so multiply by 1000: \(487 \, \mathrm{kg} \, \times \, 1000 = 487000 \, \mathrm{g}\)

Step 4: Convert liters to milliliters

To convert from liters to milliliters, multiply the number of liters by 1000. For part (d), we have 1.32 L, multiply by 1000: \(1.32 \, \mathrm{L} \, \times \, 1000 = 1320 \, \mathrm{mL}\)

Step 5: Convert deciliters to liters

To convert from deciliters to liters, divide the number of deciliters by 10. For part (e), we have 55.9 dL, divide by 10: \(55.9 \, \mathrm{dL} \, / \, 10 = 5.59 \, \mathrm{L}\)

Step 6: Convert liters to cubic centimeters

To convert from liters to cubic centimeters, multiply the number of liters by 1000. For part (f), we have 6251 L, multiply by 1000: \(6251 \, \mathrm{L} \, \times \, 1000 = 6251000 \, \mathrm{cm}^{3}\)

Key Concepts

The Metric System: An Overview

Most of the world uses the metric system for everyday measurement. It is a universal measurement system based on powers of ten. This attribute makes it particularly convenient for converting between units because you can simply move the decimal point.
Common prefixes like kilo (1000), centi (0.01), and milli (0.001) show you the magnitude of a unit. For instance, 1 kilometer is 1000 meters, and 1 kilogram is 1000 grams.
The metric system is beneficial because it simplifies calculations and eliminates complex conversion factors. Its uniformity allows for easy comparison and understanding no matter where you are, a huge advantage in science and international affairs.

Understanding Dimensional Analysis

Dimensional analysis is a mathematical technique for converting units from one system to another. This method involves multiplying the quantity you wish to convert by a conversion factor, which is a fraction equal to one and expressing the ratio between the two units.
For example, if you have a length of 25.5 meters and wish to convert it to kilometers, you would use the conversion factor of 1 km/1000 m. This conversion factor represents that 1 kilometer is equal to 1000 meters. Therefore, 25.5 meters multiplied by 1 km/1000 m equals 0.0255 kilometers.
The idea is so powerful because it ensures that your formula will always have the correct units. You multiply the original measurement unit by the right conversion factor, and the original units cancel out, leaving the new ones.

• Ensure all quantities are expressed in the same unit type before starting.
• Line up the units so they cancel appropriately in the fraction.
• Focus on keeping track of your units as much as your numbers.

Common Measurement Units in the Metric System

Measurement units in the metric system scale up or down by factors of ten, which makes them easy to understand and convert. You start by knowing the base unit and apply prefixes as necessary.
Here are common base units in the metric system:

• Meter (m) for length.
• Liter (L) for volume.
• Gram (g) for weight."

When dealing with length, you might convert from meters to kilometers, where 1 km = 1000 m.
For volume, you might convert from liters to milliliters, where 1 L = 1000 mL. And with mass, kilograms and grams are often interchanged, where 1 kg = 1000 g.
Adoption of consistent units across different fields, from science to daily life, aids in clear and concise communication. It's a globally understood language that simplifies everything from data analysis to cooking recipes.