Precision, Accuracy, Significant Figures, and Metric System Concepts

Flashcards covering precision vs. accuracy, uncertain digits and significant figures, calibration with standards, density calculations, and metric system conversions.

What is the difference between accuracy and precision as illustrated by the dartboard analogy?

Accuracy is how close measurements are to the true value (the bull’s eye). Precision is how close repeated measurements are to each other (hitting the same spot). You can be precise but not accurate, accurate but not precise, or both.

In a measurement, what is the 'uncertain digit'?

The last reported digit that is uncertain due to the instrument’s limited resolution.

What is a standard in scientific measurements and how is it used?

A carefully produced, known-value reference (like a standard solution or a weight) used to calibrate instruments and determine the true value of measurements.

If a 25 g standard reads as 24.1 g on a balance, is the balance accurate or precise?

Not accurate (reads low by about 0.9 g); it may still be precise if repeated readings cluster near each other.

If repeated balance readings for a 25 g standard are 24.0 g, 24.1 g, and 23.9 g, how would you describe the balance?

Precise (readings are close to each other) but not accurate (not at 25 g).

What are significant figures (sig figs) and why are they important?

Significant figures indicate the precision of a measurement; the last digit is uncertain. They help convey how much of the value is known.

How many significant figures are in 10.1 g and in 5.2 mL?

10.1 g has 3 significant figures; 5.2 mL has 2 significant figures.

When you multiply or divide measurements, how should you determine the number of significant figures in the result?

The result should have the same number of significant figures as the measurement with the fewest significant figures among the factors.

When you add or subtract measurements, how should you determine the number of decimal places in the result?

The result should have the same number of decimal places as the measurement with the fewest decimal places.

What is density and how is it calculated?

Density is mass per volume, calculated as density = mass ÷ volume.

Using the mass 10.1 g and volume 5.2 mL, what is the raw density and why should it be reported with limited sig figs?

Raw density ≈ 1.9423 g/mL. It should be reported as 1.9 g/mL because the volume has only 2 sig figs, limiting the precision of the result.

What is the significance of the 'metric train station' analogy?

The base unit (meter, liter, gram) is like the base station; prefixes are steps 10x up or down. Converting involves moving the decimal place by the number of prefixes crossed.

List the common metric prefixes from kilo to milli along with their exponent factors.

Kilo (10^3), Hecto (10^2), Deca (10^1), Base (10^0), Deci (10^-1), Centi (10^-2), Milli (10^-3).

What is the mnemonic commonly used to remember metric prefixes?

King Henry Died By Drinking Chocolate Milk (K, H, Da, Base, d, c, m) to recall the order of prefixes.

Convert 100 liters to kiloliters.

0.1 kiloliters (move the decimal three places to the left).

Convert 0.003 liters to milliliters.

3 milliliters (0.003 L = 3 × 10^-3 L, and 1 L = 1000 mL).

How many milliliters are in 1 deciliter?

100 milliliters (1 deciliter = 100 mL).

What prefixes beyond the basic ones were mentioned and what are their exponents?

Tera (10^12), Giga (10^9), Mega (10^6), Nano (10^-9), Pico (10^-12) were mentioned as examples of larger/smaller scales.

In the density calculation example, why is it appropriate to report density as 1.9 g/mL rather than 1.9423 g/mL?

Because the volume has only two significant figures, the density should be reported with two sig figs, giving 1.9 g/mL; reporting more would imply greater precision than the measurements support.

What is the role of standards when calibrating a balance or other measuring tools?

Standards provide a known true value (e.g., a 25 g weight) to compare against the instrument’s reading in order to assess and improve accuracy.

Why is it important to report measurements with a reasonable number of decimal places or sig figs?

To reflect the true precision of the measurements and avoid implying false certainty in the results.