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Making Measurements

Has this ever happened to you? You are baking cookies, and you mistake 1 teaspoon of vanilla for 1 tablespoon. Instead of having some nice cookies with a nice vanilla flavor, they are way too overpowered and not that great tasting. Making measurements is not only an important part of baking, but also of chemistry (and of all sciences). In this article,…

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Making Measurements

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Making Measurements
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Has this ever happened to you? You are baking cookies, and you mistake 1 teaspoon of vanilla for 1 tablespoon. Instead of having some nice cookies with a nice vanilla flavor, they are way too overpowered and not that great tasting.

Making measurements is not only an important part of baking, but also of chemistry (and of all sciences). In this article, you will learn how to make good measurements, so you can be on your way to being an awesome chemist! (and baker too!)

  • This article covers making measurements.
  • First, we will get a brief into making measurements, then learn about the metric system of measurements.
  • Next, we will learn some conversions from the US standard to the metric system.
  • Then, we will learn the basic rules of making quality measurements.
  • Thereafter, we will work on some examples to apply these rules.
  • Lastly, we will summarize why making good measurements is so important.

Making Scientific Measurements

When performing any kind of science, you will be making measurements. In chemistry, we often measure things like mass, amount, time, and so on. In this article, we will learn all about how to make good, scientific measurements and why these measurements are so important.

Making Metric Measurements

Science is a global phenomenon. All over the world, people are sharing and learning. Because of this, scientists use the International System of Units (SI) (commonly known as the metric system) as a standard, so that measurements are easily identifiable and don't need to be converted to be understood.

There are 7 basic measurements/units under this system, shown in the table below:

Figure 1-Base units of the SI (metric) system
MeasurementUnitSymbol
LengthMeterm
TimeSeconds
TemperatureKelvinK
MassKilogramkg
Amount of substanceMolemol
Electric currentAmpereA
Light (luminous) intensityCandelacd

There are some other common measurements that you will come across, such as energy (in Joules; J), volume (in Liters; L), and pressure (in atmospheres; atm), but these are considered the main standard units.

One handy thing about the metric system is that it is in base 10. This makes it easier to do calculations with, but also easier to convert between numbered units.

The metric system has a set of prefixes that denote magnitude/scale. Since it is a base 10 system, each prefix/unit is 10x greater or less than its neighbor. These prefixes are often used to "simplify" numbers. For example, 1 kilometers (km) is much easier/nicer than 1000 meters.

Below are the prefixes for units larger than the base unit (100 = 1)

Fig.2-Prefixes larger than base 10
Name of unitSymbolScientific notation/power of 10Numerical form
dekada10110
hectoh102100
kilok1031,000
megaM10410,000
gigaG105100,000
teraT1061,000,000

Let's test this out using an example:

Convert 10,000 meters to:

a) dekameters

b) kilometers

c) megameters

a) Using our chart, we see that 1 dekameter=10 meters, so:

$$10,000\,m*\frac{1\,dam}{10\,m}=1,000\,dam$$

b) 1 kilometer=1,000 meters

$$10,000\,m*\frac{1\,km}{1,000\,m}=10\,km$$

c) 1 megameter=10,000 meters

$$10,000\,m*\frac{1\,Mm}{10,000\,m}=1\,Mm$$

Now let's look at the units below the base unit:

Fig.3-Prefixes smaller than base unit
Name of unitSymbolScientific notation/Power of tenNumerical form
decid10-10.1
centic10-20.01
millim10-30.001
microμ10-60.000001
nanon10-90.000000001
picop10-120.000000000001

Like before, let's use this as an example to test your understanding:

Convert 0.00001 seconds to

a) deciseconds b) milliseconds c) nanoseconds

a) Since "deci" is 10-1, that means that it is worth \(\frac{1}{10^1}\) seconds, or to put it another way, every 10 deciseconds is 1 second, so:

$$0.00001\,s*\frac{10\,ds}{1\,s}=0.0001\,ds$$

b) 1000 miliseconds=1 seconds

$$0.00001\,s*\frac{1,000\,ms}{1\,s}=0.01\,ms$$

c) 1,000,000,000 nanoseconds=1 seconds

$$0.00001\,s*\frac{1,000,000,000\,ns}{1\,s}=10,000\,ns$$

Conversions

While scientists (and most of the world) use the metric system, here in the U.S., we use the Imperial system. Because of this, we might not always be able to make our measurements in the metric system.

For example, when you want to measure the length of something, you might pull out a ruler. Rulers measure in inches (though sometimes they may have a side for centimeters), so it's important to know how to convert between units

Here are some common conversion factors you may need to know:

  • Length:

    • Inches to centimeters: 1 inch=2.54 centimeters.

    • Miles to meters: 1 mile=1,609.34 meters.

    • Yards to meters: 1 yard=0.9144 meters.

  • Temperature:

    • Fahrenheit to Celsius: \((32^\circ F-32)*\frac{5}{9}=^\circ C\).

    • Celsius to Kelvin \(32^\circ C + 273.15=K\) (Celsius and Kelvin are both used in science, though Kelvin is considered standard).

  • Mass:

    • Pounds to kilograms: 1 pound=0.454 kilograms.

Rules in Making Measurements

When making measurements, there are a few rules we need to follow. The first rule is based on significant figures.

Significant figures (called "sig figs" for short) are the digits in a number that are considered "important" and reliable for indicating the quantity of something.

To put it in simpler terms, significant figures tell us how "sure" we are of a measurement. The more significant figures, the more precise the measurement.

So, what does this have to do with making measurements? Well, let's take a look at a common ruler:

Making Measurements A ruler StudySmarterFig.1-An image of a ruler

The numbers right above the logo are measurements in centimeters. The "notches" in between these numbers each represent 0.1 centimeters.

So let's say I was measuring a piece of metal, it lined up exactly in between the 2 and 3 marks. So, what number should I write down?

a) 2.5 b) 2.50 c) 2.5000

The answer here is b. When making measurements, the last digit is our "estimation digit". Basically, we write down our number based on the number of markings +1. The ruler has markings for centimeters (our first digit) and 0.1 centimeters (our second digit), so we are going to estimate our last digit.

When using electronic devices like a thermometer or mass balance, we use the number given. This estimation is for manual measurements

Another "rule" is for reading the volume of a liquid. When we read the volume of a liquid, we have to measure from the bottom of the meniscus.

The meniscus is the curve near the surface of a liquid caused by surface tension

When measuring volume, you always want to be at eye-level with the meniscus. Looking at a different angle may make the meniscus either harder to see or appear in a slightly different position, which could mess with your measurements.

What is the volume of this liquid?

Making Measurements Liquid meniscus StudySmarterFig.2-An example of a meniscus

Looking at the meniscus, we see the bottom of the curve is slightly between the 21 mL mark and the 21.1 mL mark. Because of this, we can estimate that the volume is 21.05 mL.

Our last "rule" is more of a rule of thumb than a set rule. We always want our measurements to be as close to the truth as possible. Because of this, it is common to make multiple measurements and then take the average.

In an experiment, there will always be "random error", which are errors that are hard to account for, such as the humidity of a room causing a sample to weigh more since it absorbed some of the moisture. Other random errors are simple human errors like marking down a number wrong.

Because of this, taking multiple measurements helps account for some errors that may occur.

Making Measurement Examples

Now that we've covered the basics of measurement making, let's work on some more examples!

What is the length of the sample?

a) In centimeters b) In millimeters

Making Measurements Ruler example StudySmarterFig.3-Measurement of a sample using a ruler

a) Looking at the tip of our sample, we see that it almost, but not quite, reaches the 4.5 cm mark. Because of this, we can estimate that our sample is 4.49 centimeters in length.

b) Since millimeters is the unit below centimeters, 10 millimeters=1 centimeter, so we just need to multiply our answer by 10, so the sample is 44.9 millimeters.

Now for an example using volume:

What is the volume of this sample?

a) 19.80 mL

b) 19.8 mL

c) 20.0 mL

d) 20.00 mL

Making Measurements Meniscus example StudySmarterFig.4-Volume measurement

Since this is a liquid, we need to focus on the bottom of the meniscus (the dip). The end of the meniscus is right on the 20 mL mark. Since the smallest markings are 0.1 mL marks, then we estimate the next digit. Therefore, our answer is d (20.00 mL).

Importance of accurancy and precision

So, why is taking measurements so important? Well, there are two main reasons: precision and accuracy.

Precision is a measure of how close a set of data points are to each other.

Accuracy is a measure of how close a set of data points are to the true value

Making sure our measurements are precise and accurate is of utmost importance. For example, imagine you worked in a lab synthesizing the key ingredient for a prescription drug. If your mass measurements were off, even by a milligram, it could have disastrous consequences for the people who rely on that drug.

Even when you are doing simple lab experiments, such as determining density, it is good practice to take the best measurements possible, so that when the stakes are raised, your work will be as accurate as possible.

Making Measurements - Key takeaways

  • Scientists use the International System of Units (SI) (commonly known as the metric system) for all their measurements
  • The basic measurement rules are:
    • When writing measurements, the number of digits is equal to the number of digits marked +1
      • Ex: If a ruler goes to the 0.01 place, we would write to the 0.001 place
    • When taking the volume of the liquid, measure from the bottom of the meniscus (curve near the top of the liquid)
    • It is good practice to take several measurements, then average them to account for possible random error
  • Precision is a measure of how close a set of data points are to each other.
  • Accuracy is a measure of how close a set of data points are to the true value

References

  1. Fig.2-An example of a meniscus (https://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Meniscus_of_water_in_burette.JPG/640px-Meniscus_of_water_in_burette.JPG) by Akaniji (https://commons.wikimedia.org/wiki/User:Akaniji) licensed by CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0/)
  2. Fig.4-Volume measurement (https://upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Meniscus.jpg/640px-Meniscus.jpg) by PRHaney licensed by CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0/)

Frequently Asked Questions about Making Measurements

When we "make a measurement" we are using a tool to quantify something based on a variable like time or length

Making measurements helps us quantify and better understand our world. We also make measurements when cooking or doing other tasks

In chemistry, we use several different tools to measure different variables, such as using beakers to measure volume.

An example of making a measurement is using a ruler to measure the length of something

We make measurements to understand the properties of elements and/or compounds. We also use it to synthesize compounds or perform certain tasks

Final Making Measurements Quiz

Making Measurements Quiz - Teste dein Wissen

Question

What is accuracy?

Show answer

Answer

Accuracy is a measure of how close measurements are to a target or accepted value

Show question

Question

What is precision?

Show answer

Answer

Precision is a measure of how close measurements are to each other

Show question

Question

Which of the following is an example of accuracy?

Show answer

Answer

Making a basket in basketball

Show question

Question

Which of the following is an example of precision?

Show answer

Answer

Redoing a problem and getting the same answer

Show question

Question

What is systematic error?

Show answer

Answer

Systematic error is caused by consistent deviations due to:
 -Personal error (such as putting the decimal in the wrong place)

-Methodological error (using wrong method, such as using the solvent)

-Instrumental error (such as being calibrated wrong)


Show question

Question

High precision, but low accuracy, is often due to what?

Show answer

Answer

Systematic error

Show question

Question

What is random error?

Show answer

Answer

Random error is caused by uncontrollable fluctuations during experimentation. Unlike systematic error, random error can fluctuate from being higher to lower than expected and can also not be replicated. An example would be copying down a measurement wrong. 

Show question

Question

What is gross error?

Show answer

Answer

Gross error is error that is significantly off due to personal error or negligence. For example, spilling a portion of your sample before measuring. 


Show question

Question

True or False: Percent error is used to calculate precision

Show answer

Answer

False

Show question

Question

A student measures the temperature of a solution and gets these measurements: 298 K, 300 K, 294 K, 300 K. If the correct temperature is 302 K, what is the percent error?

Show answer

Answer

\(1.32\%\)

Show question

Question

True or False: Standard deviation measures precision

Show answer

Answer

True

Show question

Question

A student is measuring the mass of an aluminum ball. The measurements are: 2.5 g and 2.8 g. What is the standard deviation?

Show answer

Answer

\(2.65\,g \pm 0.2\,g\)

Show question

Question

Why is a high precision, low accuracy experiment preferred to a low precision, high accuracy experiment?

Show answer

Answer

In a high precision, low accuracy experiment. There may be a systematic error occurring, which can be fixed. For a high accuracy, low precision experiment, the high accuracy may be due to chance, so the results aren't reliable

Show question

Question

A solution is referred to as a  _______ comprised of a solvent plus one or more solutes. 

Show answer

Answer

Homogenous mixture

Show question

Question

True or false: a homogenous mixture is a mixture that has a uniform composition. 


Show answer

Answer

True

Show question

Question

A _____ is a substance that is present in the highest amount, and it is used to dissolve the solute. 


Show answer

Answer

Solvent

Show question

Question

A  ____ is a substance that dissolves in the solvent and is usually present in the smallest amount. 


Show answer

Answer

Solute

Show question

Question

____ electrolytes are solutes that dissociate 100% in a given solvent.

Show answer

Answer

Strong

Show question

Question

 Solutes and solvents may be:


Show answer

Answer

 solids, liquids, or gases

Show question

Question

Solubility is defined as the _____  amount of a solute that is able to dissolve in 100 grams of water (H2O). 

Show answer

Answer

maximum

Show question

Question

True or False: Scientists use the metric system

Show answer

Answer

True

Show question

Question

What is the standard unit for length?

Show answer

Answer

Meters

Show question

Question

What is the standard unit for mass?

Show answer

Answer

Kilogram

Show question

Question

Convert 100,000 meters to gigameters

Show answer

Answer

1 Gm

Show question

Question

Convert 10 meters into kilometers

Show answer

Answer

0.01 km

Show question

Question

Convert 1000 microseconds to centiseconds

Show answer

Answer

0.1 cs

Show question

Question

What are significant figures?

Show answer

Answer

Significant figures (called "sig figs" for short) are the digits in a number that are considered "important" and reliable for indicating the quantity of something.

Show question

Question

What is the rule for significant figures when measuring?

Show answer

Answer

Number of digits=Number of digits marked by the instrument +1

Show question

Question

What is a meniscus?

Show answer

Answer

The meniscus is the curve near the surface of a liquid caused by surface tension

Show question

Question

How should a liquid be read?

Show answer

Answer

You read from the bottom of the meniscus while looking at eye-level

Show question

Question

What is precision?

Show answer

Answer

Precision is a measure of how close a set of data points are to each other.

Show question

Question

What is accuracy?

Show answer

Answer

Accuracy is a measure of how close a set of data points are to the true value

Show question

Question

Why is it good practice to take multiple measurements?

Show answer

Answer

To account for/remove error

Show question

Question

What is scientific notation?

Show answer

Answer

Scientific notation is a way to write large and/or small numbers in simpler way

Show question

Question

What is the number in front called in scientific notation?

Show answer

Answer

The coefficient

Show question

Question

True or False: A negative power means the number is a decimal

Show answer

Answer

True

Show question

Question

What are significant figures?

Show answer

Answer

Significant figures are the number of relevant digits that are reliable and necessary to express something.

Show question

Question

True or False: You can have more than one digit to the left of the decimal place.


Ex: 12.3x104

Show answer

Answer

False

Show question

Question

Convert 0.0000103 into scientific notation

Show answer

Answer

1.03x10-5

Show question

Question

Convert 1,000.5 into scientific notation

Show answer

Answer

1.0005 x 103

Show question

Question

What is the sum of these numbers?

3.67x10-3 + 1.03x10-4

Show answer

Answer

3.773x10-3

Show question

Question

____  is a branch of chemistry that deals with determining the chemical composition of a sample of material. 

Show answer

Answer

Analytical chemistry 

Show question

Question

 ____ is performed to determine what is found in a sample.


Show answer

Answer

Qualitative analysis 

Show question

Question

_____ analysis deals with the amount, concentration, or composition of a substance present. 


Show answer

Answer

Quantitative 

Show question

Question

Electrolytes are substances that conduct  _____ when dissolved in water. 

Show answer

Answer

electricity 

Show question

Question

The _______ test is used by chemists to classify substances as strong electrolytes, weak electrolytes, or non-electrolytes based on their ability to conduct electricity. 

Show answer

Answer

Conduction

Show question

Question

A _____  is a technique used to find the concentration of an unknown solution, by reacting it with a solution of known concentration

Show answer

Answer

 titration

Show question

Question

____ is an analytical technique that is used to separate a mixture into its components based on relative affinity. 

Show answer

Answer

Chromatography 

Show question

Question

Precipitation reactions are chemical reactions where a(n) _____ product (called a precipitate) is formed. 

Show answer

Answer

insoluble  

Show question

Question

Why is lab safety so important?

Show answer

Answer

There are many kinds of dangerous hazards in the lab, so following lab safety guidelines is very important

Show question

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