Scientific Measurements

Summary

The video explains how to read scales and report scientific measurements in a way that reflects an instrument’s precision. More sensitive instruments, such as an analytical balance, can provide more precise measurements than less sensitive instruments, such as a triple-beam balance.

A reported measurement has three important parts:

• Certain digits: All digits supported directly by the scale.
• Estimated digit: The final digit, estimated between scale markings.
• Uncertainty: The range of possible error. Unless stated otherwise, assume an uncertainty of ±1 in the last reported digit. An omitted uncertainty does not mean a measurement is exact.

For analog scales, the method presented is to estimate one-tenth of the distance between the smallest adjacent markings. Digital instruments generally display their precision or specify it in their manuals.

Method for Reading an Analog Scale

1. Determine the scale’s uncertainty.

   • Find the smallest adjacent scale divisions.
   • Divide the distance between them by 10.
   • Report the result as ± that amount.

2. Identify the relevant markings and certain digits.

   • Find the marks immediately below and above the point being measured.
   • Record the value supported by the lower mark as the certain portion of the reading.

3. Estimate the position between the markings.

   • Mentally divide the interval between the two marks into ten equal parts.
   • Estimate how many tenths the reading lies above the lower mark. This supplies the final, estimated digit.

4. Calculate and report the measurement.

   • Multiply the estimated number of tenths by the uncertainty.
   • Add that amount to the certain portion.
   • Include the uncertainty in the final result.

Examples

• Ruler: The blue rectangle is estimated to measure 3.27 ± 0.01 cm. The 3 and 2 are certain digits; the 7 is the estimated digit.
• Graduated cylinder: Read the bottom of the meniscus. The smallest scale divisions are 0.5 mL, so the uncertainty is ±0.05 mL. Estimating the meniscus at nine-tenths of the way from 21 to 21.5 mL gives 21.45 ± 0.05 mL.

Speakers and Sources

• Speaker: One unnamed narrator/presenter, identified by the video context as being from Ben’s Chem Videos.
• Demonstration instruments: Analytical balance, triple-beam balance, centimeter ruler, and graduated cylinder.