Scientific Measurements: Significant Figures and Measurement Errors

Question-and-Answer flashcards covering significant-figure rules, calculation guidelines, sample figure counts, and the classification, sources, and mitigation of measurement errors.

What are significant figures in a measurement?

The meaningful digits in a measured or calculated number that indicate its precision.

According to the rules of significant figures, which digits are ALWAYS significant?

All non-zero digits.

How are captive zeros treated when counting significant figures?

Zeros between non-zero digits are significant.

How are leading zeros treated when counting significant figures?

Zeros to the left of the first non-zero digit are not significant; they serve only as placeholders.

When are trailing zeros significant?

Zeros at the end of a number and to the right of a decimal point are significant.

Are final zeros to the left of an implied decimal point always significant?

Not necessarily; they may or may not be significant depending on context or notation.

In multiplication or division, how do you determine the number of significant figures in the answer?

Match the number with the fewest significant figures among the factors.

In addition or subtraction, how do you determine the number of decimal places in the answer?

Match the number with the fewest decimal places among the addends.

How many significant figures are in 3.005 g?

Four (3, 0, 0, 5).

How many significant figures are in 820 m?

Two (8, 2). The trailing zero is not to the right of a decimal point.

How many significant figures are in 0.000670 km?

Three (6, 7, 0).

How many significant figures are in 0.0405021 kg?

Six (4, 0, 5, 0, 2, 1).

How many significant figures are in 22.4 L?

Three (2, 2, 4).

What are the three main types of measurement error?

Systematic error, random error, and gross (human) error.

Define systematic error.

A consistent, repeatable error caused by faulty equipment or technique; affects accuracy.

Define random error.

An unpredictable error arising from unknown or uncontrollable factors; affects precision.

Define gross error.

A large mistake made by the user, such as misreading an instrument or recording data incorrectly.

Which type of error is predictable and can usually be corrected?

Systematic error.

Which type of error is unpredictable and hard to eliminate completely?

Random error.

Give one example of an instrumental source of error.

A miscalibrated balance (systematic error).

List two ways to minimize measurement errors in the laboratory.

Calibrate instruments regularly and avoid parallax error by viewing at eye level (other acceptable answers: practice good technique, repeat measurements, maintain consistent conditions).

A thermometer that always reads 1 °C too low is an example of which type of error?

Systematic error.

Measurements of 52.0 g, 51.9 g, and 52.1 g for a sample with a true mass of 49.0 g illustrate what error type?

Systematic error (high precision but poor accuracy).