Measurement and accuracy: obtaining data

Overview

To start the semester we will consider how scientists measure and quantify the natural world. We will learn foundational quantitative (mathematical) skills and concepts that will appear throughout the semester. We'll also consider how data is obtained using several common lab instruments.

Background

Measurement:  Accuracy & Precision [4:52]

Measurement systems:  TedED: Why the metric system matters [5:07]  &  BBC Earth Lab: A fun guide to Imperial measurements [2:50]

U.S. Metrication:  Decades TV: U.S. metrication [2:24]  &  U.S. Metric Board 1981 PSA [0:59]  &  U.S. Office of Education 1978 cartoon commercial [1:00]

Unit conversions:  The story behind the Fahrenheit [5:23]

Notation: Scientific notation [4:14]  &  Significant figures [5:03]

Article for concept application: Measurement of long-term climate trends (hurricanes) with evolving technology

Introduction

What image comes to mind when you read the word scientist? For many people, it’s a laboratory scientist with a lab coat, protective eyewear, and latex gloves. This image is frequently portrayed in textbooks, advertisements, and TV shows. This is a very specific type of scientist, one who studies microscopic objects like cells, enzymes, and DNA. However, there are many other types of scientists working in a variety of settings, using a variety of technologies, studying objects ranging from molecules to the entire planet. This semester, you’ll learn how the field of ecology blends many scientific disciplines, as well as their tools and technologies, to study all living organisms on our planet.  

The term scientist wasn't actually coined until 1834 when it was created to describe one brilliant woman, Mary Somerville, who broke the mold held at the time by “men of science”. Whereas her predecessors had largely focused their attention within one discipline, Mary Somerville was a self-taught mathematician who harmonized the fields of astronomy, geology, and biology into a single, interdisciplinary, and visionary form. Read the linked article to begin learning more about her life and her legacy. 

Ecologists today integrate many scientific disciplines, tools, and technologies to study the diversity of life on this planet. Whether it’s microbes under Antarctic ice or common cranes (birds) migrating over Mt. Everest, ecologists are driven by two key motivations: 1) describing the abundance and distribution of organisms on the planet, and 2) understanding the relationships among organisms and their environments. In this class, you’ll explore some of the most common ways ecologists measure and quantify these aspects of the natural world.  

A critical part of science is collecting data, which requires measurement.  Measurement is also critical to various other human enterprises, including trade, taxation, and construction.  Although various measurement systems exist, commonalities exist.  Most nested systems, meaning smaller standards (units) are used to measure smaller items.  For example, we use inches to measure height and miles to measure distances among cities.  They are also standardized, meaning at some level (ranging from local to global) people agree on what a measure means.  These traits are critical to making measurements useful.  

In this lab we'll discuss why the metric system is widely used globally as a measurement system.  We'll also describe how one can convert among various units (both with-in the metric system and between systems) and introduce accuracy and precision, terms that are critical to categorizing the bias and reproducibility of data.  You'll learn how to use scientific notation to write really large (or small) numbers.  Finally, we'll practice measuring by introducing common lab tools that we'll use throughout the semester.

The Metric System

The metric system, also known as the International System of Units, is an internationally known and widely used measurement system. Base units in the metric system are grams (mass, abbreviated g),  meters (length, abbreviated m), and liters (volume, abbreviated l or L).  The system is easy to use as common prefixes added to these units indicate the scale of measurement .  These prefixes are all based on the number of 10, so one can move between one metric unit by moving the decimal point and changing the associated prefix. Common prefixes include kilo (1000), milli (1/1000); others are noted below.  For example, 745 centimeters is 7.45 meters or 7450 millimeters.   

Length                                                                                                                                    Mass                                                                                                                                   Volume

1 km = 1000 meter (m)                                                                                                 1 kg = 1000 grams (g)                                                                                               1 liter (L) = 1000 mL 

1 m = 100 cm                                                                                                                      1 g = 1000 mg                                                                                                                1 mL = 1000 μL 

1 m = 1000 mm                                                                                                                 1 mg = 1000 μg                                                                                                             1 μL = 1000 nL 

1 mm = 1000 μm                                                                                                              1 μg = 1000 ng

1 μm = 1000 nm 

American Standards

Although most countries use the metric system, the United States is still practicing the older Imperial system. Below is a list of conversion factors that will help in shifting between two forms of measuring. 

Converting to and from American units and metric units seems like a daunting task but all will get better once you practice your conversions. 

Length                                                                                                        Mass                                                                                                          Volume

1 inch = 2.54 cm                                                                                   1 lb = 16 oz                                                                                             1 oz = 29.57 mL                                                    1 pint = 2 cups 

1 yd = 3 ft                                                                                                 1 gram = 0.035 oz                                                                               1 cup = 8 oz                                                             1 quart = 2 pints 

Scientific Notation 

Numbers written in scientific notation are written in the form of m * 10n (m (the coefficient) multiplied by a base (always ten in scientific notation) written in exponent form ).  m is a real number that typically only has one digit before the decimal point and the exponent n is an integer.  Since the notation is based on multiplying by a power of 10, we can move the decimal point to the right (if n is positive) or left (if n is negative).  This is useful as scientists often deal with very large or small zeros, resulting in many extra zeros that serve as placeholders.  Scientific notation also relates to the use of significant figures, or the idea that mathematical operations can't add resolution to a measurement beyond those dictated by the accuracy of the device that was used to make the measurement.  

Converting to scientific notation: 

• If you have a number between 0 and 1, form the coefficient by “moving” the decimal to the right until one non-zero digit is to the left of the decimal. For example, moving the decimal to the right of 0.0039267581 by 3 counts would place the decimal between 3 and 9.  The coefficient used in scientific notation would thus be 3.93 (three significant figures, with the last digit rounded up since the following number is greater than 4).  The value for the exponent (n)  is determined by how many places you moved the decimal and which direction.  When you move the decimal point to the right, the exponent is negative.  Therefore, final value can be written in scientific notation as 3.93 * 10-3. 

• If you have a number much greater than 1, move the decimal point to the left. For example, the coefficient used in writing 46,200,000 in scientific notation is 4.62 with the decimal point. Since you moved the decimal to the left 7 times, the exponent is positive 7. Thus, the scientific notation of 46,200,000 is 4.62 * 107. 

Converting from scientific notation: 

• If a number written in scientific notation has a negative exponent, it means that the real number is between 0 and 1. The number of the exponent will help determine the number of zeroes you will have to add in front of the first number in the coefficient before placing a decimal point.   Assuming the coefficient only has one number to the left of the digit, you will add a total number of zeroes that is equal to the (exponent - 1) to the front of the number and place the decimal point to left of all these zeroes.  For example,  8.15 *10-5 is 0.0000815 in real numbers.  4 zeroes were added because it would take 5 counts of the decimal moving to the right to get in between 8 and 1. 

• If a number is written in scientific notation using  a positive exponent, it means that the real number is much greater than 1. The number of the exponent will help determine the number of zeroes you will have to add after the last digit before placing a decimal point.  Generally, you will add (exponent  - the number of digits after the decimal in the coefficient) zeros.   For example, 7.02 *106 is 7,020,000 in real numbers.  

Methods

You'll now apply these ideas about measurement  to complete the following exercises while also learning to use common lab equipment.  Make sure to follow all safety advice provided by your instructor.  

Scientific Notation

Practice converting numbers to scientific notation in the following exercise.  Unless otherwise noted, retain 3 significant figures in the final measurement.

1. 125463            ____________________________

2. 0.0008193     ____________________________

3. 0.0000072     ____________________________

4. 149599728   ____________________________

Practice converting numbers from scientific notation in the following exercise.  Unless otherwise noted, retain 3 significant figures in the final measurement.

1. 4.87 * 109     ____________________________

2. 3.11 * 10-7     ____________________________

3. 6.80 * 104     ____________________________

4. 5.09 * 10-2     ____________________________ 

Length

Length measurements of everyday objects is usually be conducted using rulers, tape measures, or calipers. Some length measurement devices have only one unit while others have more than one. 

Answer the following questions using the yardsticks provided in class. Don’t forget the units!

1. What is your height in inches? ____________________________

2. What is your height in centimeters? ____________________________

3. What is your height in meters? ____________________________

4. Which is longer, 3 m or 30,000,000 nm? ____________________________

5. Which is shorter, 6.7 μm or 0.091 mm? ____________________________

6. What is the height of the table in feet? ____________________________

7. What is the height of the table in kilometers? ____________________________

8. What is the length of your foot in centimeters? ____________________________

9. What is the length of your foot in feets? ____________________________

10. What is the length from your wrist to the bend of your elbow in centimeters? ____________________________

11. Convert the previous length to yards. ____________________________ 

Between your foot and arm (wrist to elbow), which is longer? ____________________________ 

Using a balance or a scale is an important skill in a science laboratory setting and weighing something accurately requires practice. To operate the electronic scale in this lab, exercise the following steps:

1. Observe the scale you will be using. Look for a note on the maximum weight the scale can measure.  What is it? Exceeding this limit can damage the scale and will lead to an error message appearing on the display.

2. Connect the scale to a power outlet in the lab.

3. Turn on the scale by pressing down on the ON/OFF button on the scale (it may take a couple of seconds before the text appears on the screen). 

4. Allow the scale to “adjust” itself before using (the screen may show a countdown before the scale is ready).

5. The default unit of the scale is set to grams (the letter “g” on the screen), make sure this is correct. If the unit is not in grams, you can change it by pressing the “CAL” or “MODE” button until the “g” appears. 

6. Without any objects or force on the scale, the screen should read 0.0g. If it does not, press on the “ZERO” or “TARE” button once. This will deduct any weight on the scale and return it to zero. 

7. Now you are ready to weigh! Make sure to place the objects on the center of the scale for an precise measurement.

Taring the scale is also useful for weighing liquids or hard to measure items (like grains of salt, mud, or dirt) since it allows you to deduct the weight of the container that is holding the items to be measured; this also helps keeps the scale clean.  For example, if the object you are weighing is sugar or salt, you may want use a weigh tray to hold the substance but do not want to add in the weight of the tray or contaminate the scale. Thus, weighing the tray first (without any substance) and pressing the “TARE” button will ignore the weight of the tray and only measure the mass of the substance after you weigh the substance with the tray. Note that the container weight still counts toward the maximum weight the scale can measure, so  use caution in measuring larger quantities.

Practice operating the scale with the following exercise, don’t forget your units.

1. What is the mass of your cell phone with the case on in grams? ____________________________

2. What is the mass of only your cell phone case in grams? ____________________________

3. Calculate the mass of your cell phone in grams by subtracting the weight of the cell phone case from the weight of the cell phone with the case on. ____________________________

4. Weigh the cell phone without the case on and compare this to the measured mass of your cell phone, is it different?  ____________________________

5. Now let’s practice with the “TARE”  button, which can removed the need to do tedious calculations like we did above. Place only your cell phone case on the scale and tare the balance. Snap your case back on and reweigh the cell phone and the case. What is the mass of the your cell phone? ____________________________

6. Check with the answer from the previous question, is it the same? ____________________________.  Note that tare zero's out whatever weight you have on the scale.

7. Convert the mass of your cell phone to ounces. ____________________________

8. Now, look up the nutritional facts on the side of the beverage provided to you (can/bottle of soda). How many grams of sugar are in the beverage? ____________________________

9. Place the blue plastic weighing tray on the scale and measure it.  What is the mass of the weighing tray in grams? ____________________________

10. Now tare the scale and add the amount of sugar noted on your beverage container. 

11. Now remove the weighing tray and sugar from the scale. What weight is shown on the display?  Why?   ____________________________

12. Dr. Seuss gave you your cold medicine and warned you against overmedicating as the side effects could be harmful. The instructions from Dr. Seuss were to take only half a gram, no more and no less. When you get home, you found that the print on your cold medicine says:  “Take with caution and follow doctor’s advice. Each spoonful contains 50 mg.”

How many spoonfuls should you take? ____________________________

Temperature

Temperature is also another important measurement we use in our everyday life and in scientific laboratories. Temperature is a quantity that expresses how cold or hot something is.  Temperature is measured using a thermometer.There are 3 scales for temperature that are widely used in science: Kelvin, Fahrenheit, and Celsius (also known as Centigrade). For this lab, we will focus on the last two. Fahrenheit is official temperature scale in the United States, while the rest of world mainly uses Celsius. One can convert between the two scales using the following formulas:

°C = (°F - 32) * (5/9)                                                                      °F = (°C) * (9/5) + 32

*Make sure to calculate things in the parenthesis first because PEMDAS (order of operations). 

Work on the following exercise to check for your understanding of the formulas.

1. Water boils at 100°C, what is the boiling temperature in Fahrenheit? ____________________________

2. Normal human body temperature is 98.6°F. Convert the normal human body temperature from Fahrenheit to Celsius. ____________________________

Familiarize yourself with a thermometer by working on the following questions. Make sure you treat the thermometers with care.