Question

Perform the following conversions from non-SI to SI units. (Use information from the inside back cover, as needed.) (a) 68.4 in. \(=\)________cm (b) \(94 \mathrm{ft}=\)________m (c) \(1.42 \mathrm{lb}=\)________g (d) \(248 \mathrm{lb}=\)________kg (e) \(1.85 \mathrm{gal}=\)________dm\(^3\) (f) \(3.72 \mathrm{qt}=\)________mL

Short answer

a) 173.736 cm, b) 28.6512 m, c) 644.101158 g, d) 112.490708 kg, e) 7.0530095 dm^3, f) 3523.912076 mL

Step-by-step solution

Convert inches to centimeters

To convert inches to centimeters, the conversion factor to remember is 1 inch equals 2.54 centimeters. Multiply the presented value in inches (68.4 in) by 2.54 to convert to centimeters.

Convert feet to meters

To convert feet to meters, the conversion factor to remember is 1 foot equals 0.3048 meters. Multiply the presented value in feet (94 ft) by 0.3048 to convert to meters.

Convert pounds to grams

To convert pounds to grams, the conversion factor is 1 pound equals 453.59237 grams. Multiply the value in pound (1.42 lb) by 453.59237 to convert it to grams.

Convert pounds to kilograms

For converting pounds to kilograms, the conversion factor is 1 pound equals 0.45359237 kilograms. Multiply the value in pound (248 lb) by 0.45359237 to convert it to kilograms.

Convert gallons to cubic decimeters (litres)

To convert gallons to cubic decimeters (litres), the conversion factor is 1 gallon equals 3.78541 dm^3. Multiply the value in gallons (1.85 gal) by 3.78541 to convert to cubic decimeters.

Convert quarts to milliliters

For converting quarts to milliliters, the conversion factor is 1 quart equals 946.352946 ml. Multiply the provided value in quarts (3.72 qt) by 946.352946 to convert to milliliters.

Key concepts

Unit Conversion

Unit conversion is pivotal when calculations involve quantities expressed in different systems of measurement. The most common reason for converting units is to facilitate a clearer understanding of data by using internationally recognized standards, like the metric system.

To effectively perform unit conversions, follow these steps:

• Identify the original and target units.
• Locate a reliable conversion factor. For instance, the exercise above uses several conversion factors like 1 inch equals 2.54 centimeters or 1 gallon equals 3.78541 cubic decimeters.
• Multiply the original measurement by this conversion factor to get the measurement in the target unit.

Using precise conversion factors ensures accuracy, especially in scientific and technical fields where minute differences can significantly impact outcomes.

Metric System

The metric system, also known as the International System of Units (SI), is a decimal-based system of measurement used globally. Designed to simplify and standardize measurements, it is widely adopted in science, industry, and commerce. The system is based on units that increase or decrease in magnitude by a factor of ten, making calculations straightforward.

Key elements of the metric system include:

• Base units like meter (m) for length, kilogram (kg) for mass, and liter (L) for volume.
• Prefixes that indicate orders of magnitude. For example, the prefix 'centi-' means one-hundredth, so a centimeter (cm) is one-hundredth of a meter.

Having a unified measurement system reduces confusion and errors, particularly in fields that rely on precise data interpretation, such as engineering and examination of scientific phenomena.

Dimensional Analysis

Dimensional analysis, also known as factor-label method, is a technique for converting between units using conversion factors arranged in a manner that allows units to "cancel" out during calculations. This method ensures that equations are dimensionally consistent, helping to verify calculations intuitively and avoiding conversion mishaps.

To perform dimensional analysis:

• Write down the quantity to be converted and identify its unit.
• Multiply by conversion factors in a fraction format, where the numerator and denominator are equivalent but in different units, e.g., \( \frac{2.54\text{ cm}}{1\text{ in}} \).
• Ensure that all unwanted units cancel out, leaving the equation with the desired units.

By carefully managing units throughout the calculation process, dimensional analysis can simplify complex conversions and serve as a powerful tool for problem-solving in physics and chemistry.