Working with Measured Numbers in Science
The foundation of science has been built on data collected from the world. This data can take two forms: qualitative and quantitative. Qualitative data is descriptive information about something, such as its color, smell or shape. Quantitative data is statistical information measured using numbers and values. When quantitative data is collected during an experiment, a scientific instrument is usually used. Metric rulers, graduated cylinders, thermometers, and balances, just to name a few, are instruments that could be used to collect quantitative data during an experiment.
When quantitative data is collected, the precision of the instrument is very important to consider. Why is this? Because the precision of the instrument determines the precision of the data. For example, look at the two centimeter rulers surrounding the strip of grey metal. (shown in the diagram below). Ruler A has graduated marks to the TENTHS place, while ruler B has graduated marks only to the ONES place. This means ruler B is LESS precise than ruler A. More importantly, this means using ruler A will enable you to collect more precise data about the length of that piece of metal, than ruler B.
Using Ruler A, the length of the metal would be estimated to be about 3.22 centimeters. This is 3 significant digits (2 measured numbers + 1 estimated number) Using Ruler B, the length of the metal could be estimated one place value less precise, with an estimated length of about 3.2 centimeters. This is 2 significant digits (1 measured numbers + 1 estimated number).
All measurements will go one place value more precise then the last place value marked on the instrument (because of the estimate). So looking at the chart below you will see some examples of what place values, the data would have, based on the instrument’s precision.
So for example, look at the graduated cylinder shown below.
The graduated cylinder above has marked measurements to the ONES PLACE. This means with an ESTIMATED DIGIT, the final measurement of water, should be one place value more precise then the marks on the instrument, which would be the TENTH PLACE .
So a proper measurement for the water found in this graduated cylinder would be 18.5 mL. This final measurement has 3 significant digits (2 measured numbers + 1 estimated number). This final measurement goes to the tenth place.
Let's look at two more examples of this idea. First, lets study the beaker shown below.
Example #1
To what place value does the beaker have measurements?
ANSWER: tens places
What would be a proper measurement of the volume of this water?
58 mL
* the measurement should be one place value estimated past the last place value visible on the measuring device.
Now lets take a look at the thermometer below.
Example #2
To what place value does the thermometer have measurements?
ANSWER: ones place
What would be a proper measurement of the temperature?
44.5 degrees Celsius
* the measurement should be one place value estimated past the last place value visible on the measuring device.
