Question

Write the equality and conversion factors for each of the following: a. centimeters and inches b. pounds and kilograms c. pounds and grams d. quarts and liters e. dimes in 1 dollar

Short answer

1 inch = 2.54 cm, 1 lb = 0.453592 kg, 1 lb = 453.592 g, 1 quart = 0.946353 L, 1 dollar = 10 dimes.

Step-by-step solution

Centimeters and Inches

1 inch equals 2.54 centimeters. The equality is: \(1 \text{ inch} = 2.54 \text{ cm}\)Conversion factors are:\[ \text{To convert inches to cm:} \frac{2.54 \text{ cm}}{1 \text{ inch}} \]\[ \text{To convert cm to inches:} \frac{1 \text{ inch}}{2.54 \text{ cm}} \]

Pounds and Kilograms

1 pound equals 0.453592 kilograms. The equality is: \(1 \text{ pound} = 0.453592 \text{ kg}\)Conversion factors are:\[ \text{To convert pounds to kg:} \frac{0.453592 \text{ kg}}{1 \text{ pound}} \]\[ \text{To convert kg to pounds:} \frac{1 \text{ pound}}{0.453592 \text{ kg}} \]

Pounds and Grams

1 pound equals 453.592 grams. The equality is: \(1 \text{ pound} = 453.592 \text{ g}\)Conversion factors are:\[ \text{To convert pounds to grams:} \frac{453.592 \text{ g}}{1 \text{ pound}} \]\[ \text{To convert grams to pounds:} \frac{1 \text{ pound}}{453.592 \text{ g}} \]

Quarts and Liters

1 quart equals 0.946353 liters. The equality is: \(1 \text{ quart} = 0.946353 \text{ L}\)Conversion factors are:\[ \text{To convert quarts to liters:} \frac{0.946353 \text{ L}}{1 \text{ quart}} \]\[ \text{To convert liters to quarts:} \frac{1 \text{ quart}}{0.946353 \text{ L}} \]

Dimes in 1 Dollar

1 dollar equals 10 dimes. The equality is: \(1 \text{ dollar} = 10 \text{ dimes}\)Conversion factors are:\[ \text{To convert dollars to dimes:} \frac{10 \text{ dimes}}{1 \text{ dollar}} \]\[ \text{To convert dimes to dollars:} \frac{1 \text{ dollar}}{10 \text{ dimes}} \]

Key concepts

Unit Conversion

Unit conversion is a fundamental concept in chemistry and everyday life. Understanding this helps convert one type of measurement to another easily.
It uses a conversion factor, a ratio that expresses the relationship between two units. For example, if you know that 1 inch equals 2.54 centimeters, you can convert inches to centimeters by multiplying the number of inches by 2.54.
Here's how you apply it:

• Identify the conversion factor.
• Multiply or divide by the conversion factor.

Converting between metric and imperial units, like inches to centimeters, often requires remembering a few key numbers.

Metric System

The metric system is a decimal-based system of measurement used worldwide. It simplifies calculations by using base units and prefixes. Base units include meters (for length), grams (for mass), and liters (for volume).
For example, 1 meter equals 100 centimeters, and 1 kilogram equals 1000 grams. This makes it easier to convert between units by simply moving the decimal point.

• Prefixes like kilo-, centi-, and milli- help indicate the scale.
• Understand that the system is interrelated, making conversions straightforward within the metric itself.

This consistent structure is why it's preferred in scientific measurements.

Dimensional Analysis

Dimensional analysis (often called factor-label method) is a technique for solving problems by using the units of the given information. It's particularly useful for unit conversions and ensuring equations make sense.
This involves multiplying by conversion factors set up as fractions so units cancel appropriately:

• Write down the quantity you start with.
• Multiply by conversion factors arranged so units cancel out.
• Continue until you reach the desired unit.

For example, to convert 10 inches to centimeters: \( 10 \text{ in} \times \frac{2.54 \text{ cm}}{1 \text{ in}} = 25.4 \text{ cm} \).
Each step ensures the units check out, offering a systematic approach to conversions.

Measurement Units

Measurement units provide a standard for quantifying physical properties, such as length, mass, and volume. These units make it possible to discuss and compare measurements reliably.
Examples include inches, pounds, liters, and grams. Each belongs to a specific measurement system:

• Imperial (inches, pounds, quarts).
• Metric (centimeters, grams, liters).

Knowing these units and their relationships is crucial in science and daily tasks.
For instance, knowing that 1 pound equals 453.592 grams can help when cooking or doing scientific experiments.
Mastery of measurement units and their conversions ensures accuracy and understanding in various contexts.