September 21st - Error, Uncertainty, and Prefixes

Today, as the title suggests, we learned about the types of error, the possible causes of error, the uncertainty principle, and SI prefixes.

The class started with a collection of the chemical balancing worksheet that was for homework. Next, we got into groups of 2 or 3 and were out handed a worksheet. We were instructed to use our textbooks and any other resources we could find to answer the questions on the worksheet. 

The first section of the worksheet asked us to list 13 common SI prefixes, their symbols, and their multipliers. The SI prefixes are:

The above diagram also lists one bonus SI prefix! The smallest of the listed divisions, 'atto-', can be symbolized by the lower-case letter 'a'. It's multiple is 10⁻¹⁸ (fun fact: 'atto' is derived from the Danish word atten, meaning "eighteen"). 

In Chemistry 11, the five prefixes that we will use the most are 'mega-' (M, 10⁶), 'kilo-' (m, 10³), 'centi-' (c, 10⁻²), 'milli-' (m, 10⁻³), and 'micro-' (μ, 10⁻⁶).

Our next task was to list at least one example of a place where each prefix is used. Here are a select few that came up with:

• 'femto-' is used in the term 'femtotechnology' (technology on the scale of a femtometre)
• 'tera-' and 'giga-' are used in the terms 'terabyte' and 'gigabyte' (used for digital information storage)
• 'kilo-' and 'milli-' are used in the terms 'kilogram' and 'milligram' (used to measure mass)
• 'nano-' and 'micro-' are used in the terms 'nanosecond' and 'microsecond' (used to measure time)

The next major topics of the day were accuracy, precision, and error. Accuracy refers to how close measurements are to the expected value. Precision refers to how close measurements are to each other. In the image below, you can see the difference between precise throws and accurate throws in a game of darts:

Now that we know what precision and accuracy are, we can learn about error. Error refers to the amount by which a sample differs from its expected value. Error and accuracy can be expressed through either absolute error or percent error. Absolute error refers to the difference between the measured value of a quantity and the actual value. It can be calculated with the following formula:

Percent error refers to the percentage given by dividing the absolute error by the accepted measurement, then multiplying the quotient by 100, like so:

It is important to note that error is inescapable in science. Measuring instruments are never completely free of flaws, so the measurement will always be off (the amount it is off depends on the specific instrument). Ambient conditions may change during an experiment. Human error could also occur in estimation. Estimation is always used in measurement (the amount of estimation depends on the specific instrument).

To acknowledge error, a plus-minus sign (±) is used when giving a measurement. For example, on some graduated cylinders, the smallest division is 1mL (please note that the measurement of water in a graduated cylinder is always taken from the bottom of the mensicus, which is the curved surface of a liquid in a container). An appropriate error measurement for this particular graduated cylinder would be ±0.5mm. To calculate the error measurement, you simply divide the smallest division of the instrument by 2.

The last thing we learned about was the Heisenberg uncertainty principle. This principle states that no matter how hard you try, experiments will always be affected by those who perform them. In some way, shape, or form, you are changing the experiment. For example, if you add light for better observation, you can influence the behaviour of quanta (quantum particles). If you want to know the velocity of a quark, you have to measure it. In order to measure it, you have to add energy. For this reason, scientists can never be certain that their answer is completely accurate. Here's an in-depth look at the principle:

 Posted by Michael.