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Chapter 8: Problem 1

Define the key terms. a. Unit of measure b. Conversion factor c. Unit ratio (or unit fraction)

Short Answer

Expert verified
Unit of measure: Standard quantity; Conversion factor: Numerical factor for unit change; Unit ratio: Fraction to convert units.

Step by step solution

01

Define 'Unit of measure'

A unit of measure is a standard quantity used to specify a physical quantity. Examples include meters for length, kilograms for mass, and seconds for time.
02

Define 'Conversion factor'

A conversion factor is a numerical factor used to multiply or divide a quantity when converting from one unit to another. For example, to convert inches to centimeters, the conversion factor is 2.54 (since 1 inch = 2.54 cm).
03

Define 'Unit ratio (or unit fraction)'

A unit ratio (or unit fraction) is a fraction that represents the relationship between two units, showing how many of one unit equals one of another. For example, the unit ratio for converting hours to minutes is: \( \frac{60 \text{ minutes}}{1 \text{ hour}} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Unit of measure
Units of measure are the fundamental building blocks in the field of measurements. They provide a standard to quantify physical quantities, allowing us to compare, communicate, and compute various amounts effectively. For instance, when we talk about distance, the meter is a common unit of measure. Another example is the kilogram, which is the standard unit for mass.

Units help in ensuring everyone is on the same page while assessing a given quantity. This standardization is crucial for scientific experiments, construction, and everyday activities like shopping.
  • Meter (m) for length
  • Kilogram (kg) for mass
  • Second (s) for time
Conversion factor
A conversion factor is a numerical approach used to change a quantity from one unit to another. It is essential because not all measurements are made using the same units. For example, when you have a length measured in inches but need it in centimeters, you use a conversion factor.

The conversion factor between inches and centimeters is 2.54. This means 1 inch is equal to 2.54 centimeters. To convert inches to centimeters, you simply multiply the inches by 2.54. Conversely, to convert centimeters to inches, you would divide by 2.54.
  • To convert miles to kilometers, the conversion factor is 1.609.
  • For converting pounds to kilograms, the conversion factor is 0.453592.
Unit ratio (or unit fraction)
A unit ratio, sometimes referred to as a unit fraction, is a fraction that shows the equivalence between two different units of measure. It acts as a handy tool to switch between units, providing a clear relationship between them.

For example, to convert hours to minutes, the unit ratio is \(\frac{60 \text{ minutes}}{1 \text{ hour}}\). This notation means there are 60 minutes in every 1 hour. When you multiply a quantity by this fraction, you change the units without altering the value.
  • For converting days to hours: \(\frac{24 \text{ hours}}{1 \text{ day}}\).
  • When converting feet to inches: \(\frac{12 \text{ inches}}{1 \text{ foot}}\).
Physical quantity
A physical quantity is any property or characteristic of a material or system that can be measured or quantified. Physical quantities are essential in science and engineering as they allow us to describe and understand various phenomena in the natural world.

For example, physical quantities include:
  • Length
  • Mass
  • Time
  • Temperature
  • Electric current
These quantities are typically measured using standard units of measure, such as meters for length, which helps ensure consistency and accuracy in data collection and communication across different fields and applications.

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Most popular questions from this chapter

A tennis court is \(120 \mathrm{ft}\) long and \(60 \mathrm{ft}\) wide. What is the length of the diagonal? Round to the nearest hundredth of a foot.

Convert the units of area by using multiple factors of the given unit ratio. $$54 \mathrm{ft}^{2}=\quad y \mathrm{d}^{2}\left(\text { Use two factors of the ratio } \frac{1 \mathrm{yd}}{3 \mathrm{ft}}\right)$$

A roll of ribbon is 60 yd. If you wrap 12 packages that each use 2.5 ft of ribbon, how much ribbon is left over?

Fill in the blank with \(>,<,\) or \(=\) $$1 \mathrm{mL}______1 \mathrm{cc}$$

A 24 -fl-oz jar of spaghetti sauce sells for \(\$ 2.69 .\) Another jar that holds \(1 \mathrm{qt}\) of sauce sells for \(\$ 3.29 .\) Which is a better buy? Explain.
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