Instruments and Measurements (Week 1): Units and Measurements

What are the two main components of any measurement?

A numerical value and a unit.

Define accuracy in the context of measurements.

Accuracy is how close a measurement is to the true or accepted value.

Define precision in the context of measurements.

Precision is how close repeated measurements are to each other.

How does accuracy differ from precision?

Accuracy reflects closeness to the true value; precision reflects consistency.

Why can no measurement be perfectly accurate?

All measurements are affected by limitations in instruments or human error.

What are the two main types of measurement errors?

Random errors and systematic errors.

How do random errors affect measurements?

They cause measurements to vary unpredictably around the true value.

How do systematic errors affect measurements?

It causes either undermeasurement or overmeasurement of the true value of an object and leads to inaccuracies in data, impacting the reliability of results.

Give an example of a random error in measuring mass.

Wind vibrations during weighing causing fluctuation in balance readings/Evaporation of Liquid Inside a Beaker During Weighing, causing a loss in mass and inaccurate measurement.

Give an example of a systematic error in measuring length.

Using a ruler that's worn down at one end, leading to consistent under-measurement.

How can random errors be minimized?

By taking multiple readings and averaging them.

Why can’t systematic errors be reduced by averaging?

Because the error is consistently biased in one direction.

Name a common cause of systematic errors in lab instruments.

Poor calibration of instruments.

How can systematic errors be eliminated?

By recalibrating instruments or using properly calibrated tools.

What is parallax error?

An apparent shift in the position of an object due to a change in observer position.

How does parallax error occur when using a ruler?

By not viewing the scale directly above the measurement mark.

How can parallax error be avoided when reading an analog scale?

By ensuring your eye is level with the measurement marking.

Why are digital readouts less prone to parallax error?

Because they display a fixed numeric value that isn’t influenced by viewing angle.

Describe how to correctly read the volume of water in a graduated cylinder to avoid parallax error.

View the meniscus at eye level and read the bottom of the curved surface.

What is the meniscus, and how does it affect volume measurements?

The curved surface of a liquid; volume should be read at the bottom of the meniscus.

What is the purpose of calibrating a measuring instrument?

To ensure it gives accurate readings by comparing it to a known standard.

How often should instruments be calibrated?

Regularly, depending on frequency of use and manufacturer recommendation.

What is a "standard" in the context of calibration?

A known, accurate reference used to adjust instruments.

Why is calibration critical for scientific experiments?

To ensure data reliability and minimize systematic errors.

Name an instrument that commonly requires calibration.

Balance (weighing scale).

What do significant figures represent in a measurement?

They indicate which digits are meaningful and reflect measurement precision.

How does the number of significant figures relate to precision?

More significant figures indicate a higher level of precision.

Write 0.0045060 in scientific notation and state its significant figures.

4.5060 × 10⁻³; 5 significant figures.

How many significant figures are in 2500 vs. 2500.0?

2500 has 2–4 significant figures (ambiguous); 2500.0 has 5.

Why is scientific notation useful for indicating significant figures?

It clearly shows which digits are significant.

What is the rule for significant figures in multiplication/division?

The result should have the same number of significant figures as the factor with the fewest.

What is the rule for significant figures in addition/subtraction?

The result should match the least number of decimal places.

Solve: (6.038 × 2.57) and report the answer with correct significant figures.

15.5 (3 significant figures).

Solve: (20.0 cm + 100.22 cm) and report the answer with correct significant figures.

120.2 cm (3 significant figures).

Why should rounding only be done at the end of calculations?

To avoid rounding errors from accumulating during intermediate steps.

Convert 3 weeks into milliseconds.

1.8144 × 10⁹ ms.

Convert 38.1 ft/s to miles/hour.

38.1 ft/s = 25.98 mph.

Convert 554 m⁴/(day·kg) to cm⁴/(min·g).

3.855 × 10⁷ cm⁴/(min·g).

Convert 760 miles/hour to m/s.

339.04 m/s.

Convert 921 kg/m³ to lbm/ft³.

57.5 lbm/ft³.

Convert 5.37 × 10³ kJ/min to horsepower (hp).

119.9 hp.

Convert 6 (in)(cm²)/(yr)(s)(lbm)(ft²) to SI units.

9.85 × 10⁻⁵ m³/s·kg.

What does dimensional consistency mean in equations?

Each term in an equation must have the same units.

For the equation r = 200D – 10D² (r in crystals/min, D in mm), what are the units of 200 and 10?

200 has units of crystals/min·mm, and 10 has units of crystals/min·mm².

Calculate the nucleation rate (crystals/s) for a crystal diameter of 0.050 inches using the equation r = 200D – 10D².

r = 200(1.27 mm) – 10(1.27 mm)² = 254 – 16.13 = 237.87 crystals/min = 3.965 crystals/s. (remember to round up)