Recording Measurements with Uncertainties

When reading an analog instrument like a burette, you read from the bottom of the meniscus. The last digit recorded is your best guess. For example, if the meniscus is exactly on 20.0, you would record 20.00 mL because the instrument can measure to a hundredth of a milliliter. If it's between 20.0 and 20.1, you might estimate 20.05 mL, with the '5' being the best guess.

For glass instruments such as a burette or a graduated cylinder, the uncertainty is typically half of the smallest increment. If the smallest increment is 0.1 mL, the uncertainty is ±0.05 mL. So, a reading of 20.00 mL would be recorded as 20.00 ± 0.05 mL.

Similar to other analog instruments, when measuring with a ruler, you determine the certain digits and then make an estimation for the last digit. If the smallest subdivision is a millimeter (0.1 cm), your measurement would include a best-guess digit in the hundredths place. The uncertainty would be half of the smallest subdivision, which is ±0.05 cm.

For digital instruments like an electronic balance, the uncertainty is usually considered to be in the last displayed place value. If the balance reads 175 grams (ones column), the uncertainty would be ±1 gram, indicating the actual mass could be between 174 and 176 grams. If it reads 0.98 grams (hundredths column), the uncertainty would be ±0.01 grams, meaning it could be between 0.97 and 0.99 grams. Some devices may have their uncertainty specified on the device or its documentation.

When recording multiple trials in a lab report, you don't need to write the uncertainty after every single measurement. Instead, you can state the uncertainty once at the top of the column for that specific measurement. This indicates that all values in that column share the same uncertainty.