In July 1983, an Air Canada Boeing 767 ran out of fuel halfway through a flight from Montréal to Edmonton. The ground crew had worked out the fuel in pounds when the new plane's system needed kilograms, so the plane carried less than half the fuel it needed. The pilots glided it to a safe landing on an old airstrip at Gimli, Manitoba, and the plane became known as the "Gimli Glider". Numbers in science mean nothing without the right units, and a measurement is only as good as the way it was taken. This lesson covers the measuring, recording and graphing skills you will use in every lab.
SI units and prefixes
| Quantity | SI unit (symbol) | Measured with |
|---|---|---|
| Length | metre (m) | Ruler, metre stick, measuring tape |
| Mass | kilogram (kg); in labs often gram (g) | Electronic or triple-beam balance |
| Time | second (s) | Stopwatch, timer |
| Temperature | kelvin (K); in labs usually degree Celsius (°C) | Thermometer, temperature probe |
| Volume (of liquids) | cubic metre (m³); in labs usually litre (L) or millilitre (mL), where 1 mL = 1 cm³ | Graduated cylinder, beaker (rough only) |
| Prefix | Symbol | Means | Example |
|---|---|---|---|
| kilo | k | 1000 times the base unit | 1 km = 1000 m |
| (base unit) | 1 | 1 m, 1 g, 1 L | |
| centi | c | one hundredth (0.01) | 1 cm = 0.01 m, so 100 cm = 1 m |
| milli | m | one thousandth (0.001) | 1 mL = 0.001 L, so 1000 mL = 1 L |
| micro | µ | one millionth (0.000 001) | 1 µm = 0.000 001 m; a bacterium is a few µm long |
Reading instruments, accuracy and precision
Report a measurement to the precision of your instrument. For a scale with markings (a ruler or thermometer), read to the smallest marking and then estimate one more digit between the marks. A ruler marked in millimetres can be read to a tenth of a millimetre by eye, such as 4.35 cm. For a digital instrument, record every digit it shows. For a graduated cylinder, read the bottom of the curved surface of the liquid (the meniscus) with your eye level with it. Writing 4.35 cm instead of "about 4 cm" tells the reader how carefully you measured.
- How close a measurement is to the true or accepted value
- Improved by calibrating instruments and fixing errors in method
- Example: three readings of 99.8 °C, 100.3 °C and 100.1 °C for boiling water at sea level are accurate
- How close repeated measurements are to each other, and how fine the instrument's scale is
- Improved by careful technique and finer instruments
- Example: readings of 5.42 g, 5.41 g and 5.43 g are precise, even if the true mass is 6.00 g (then they are precise but not accurate)
To judge accuracy with a number, scientists calculate percent error: how far the measured (experimental) value is from the accepted value, as a percentage of the accepted value. The bars mean "take the size of the difference and ignore the sign", so percent error is never negative. A smaller percent error means a more accurate result.
Data tables and graphs
| Volume of water (mL) | Mass of water (g) |
|---|---|
| 10.0 | 10.1 |
| 20.0 | 19.8 |
| 30.0 | 30.2 |
| 40.0 | 39.9 |
| 50.0 | 50.3 |
- Put the independent variable on the x-axis (horizontal) and the dependent variable on the y-axis (vertical).
- Label each axis with the quantity and its unit, such as "Volume (mL)".
- Choose an even scale on each axis (every square worth the same amount, like 5 mL) that uses most of the grid.
- Give the graph a title, usually "Dependent variable vs independent variable", such as "Mass vs Volume of Water".
- For data that follow a trend, draw a line of best fit: one smooth straight line (or curve) with about as many points above it as below. It does not have to pass through every point, through the first and last points, or through the origin (0, 0).
A line of best fit lets you make predictions. Interpolation means reading a value between your measured data points, such as the mass of 25 mL of water. It is usually reliable, because you are inside the range you tested. Extrapolation means extending the line beyond your data, such as predicting the mass of 500 mL. It is riskier, because the pattern might change outside the range you measured. Points far from the line, called outliers, may come from a measuring mistake. Check them, and do not let one outlier pull your line off the trend.