Question

a. Define conversion factor. b. Explain how conversion factors are used.

Short answer

A conversion factor is a ratio for converting units. Multiply the quantity by the conversion factor to change units.

Step-by-step solution

Define Conversion Factor

A conversion factor is a ratio or fraction which represents the relationship between two different units. It is used to convert quantities from one unit of measurement to another. For example, the conversion factor from inches to centimeters is 2.54 cm per inch.

Understanding the Use of Conversion Factors

To use a conversion factor, multiply the quantity you have by the conversion factor to get the quantity in the desired unit. The goal is to cancel out the original units, leaving the desired units. For instance, if you want to convert 10 inches to centimeters, you would multiply 10 inches by the conversion factor of 2.54 cm/inch, which equals 25.4 cm.

Example of Conversion

If you need to convert 5 miles into kilometers, and you know the conversion factor is 1 mile = 1.60934 kilometers, you multiply 5 miles by 1.60934 km/mile to get 8.0467 kilometers.

Key concepts

Unit Conversion

Unit conversion is the process of changing a measurement from one unit to another. This is important in everyday life and in science. For instance, you might need to convert miles to kilometers for a road trip. To do a unit conversion, you use a conversion factor. This is a special ratio that tells you how many of one unit equals another unit. The key is to multiply by the right conversion factor. This changes the units but keeps the same quantity.
Imagine you need to convert 10 feet into inches. Since there are 12 inches in a foot, your conversion factor is 12 inches/1 foot. You would multiply 10 feet by the conversion factor (12 inches/1 foot) and get 120 inches. This way, you've just changed the units from feet to inches while keeping the measurement accurate.

Measurement

Measurement is determining the size, length, or amount of something. It is a fundamental concept in science and daily life. Measurements use units to express quantities. Different systems of measurement exist, such as the metric system (meters, liters, grams) and the imperial system (feet, gallons, pounds). To ensure accuracy, always use the same units or convert them when needed.
For example, if you're baking a cake, you need precise measurements. You might have a recipe in cups but your measuring tools are in milliliters. Here, you’d use a conversion factor to switch from cups to milliliters. One cup equals 237 milliliters. So, if you need 2 cups, you'd multiply 2 by 237 to get 474 milliliters.

Ratios

A ratio is a way to compare two quantities by showing the relative size of one quantity to another. Ratios can be written in three ways: using the word 'to' (3 to 4), a colon (3:4), or as a fraction \(\frac{3}{4}\). Ratios are incredibly useful in understanding relationships between numbers and for making conversions.
For example, the conversion factor itself is a type of ratio. Combining this with unit conversion, if you have 60 seconds, and want to know how many minutes that is, you'd use the ratio of minutes to seconds (1 minute to 60 seconds). By setting up this ratio, you can find out that 60 seconds equals 1 minute by dividing 60 by 60. Understanding ratios helps you compare quantities easily and perform conversions more accurately.