Chapter 1-7 Significant Figures Review Flashcards

A set of 30 vocabulary flashcards covering significant figures rules, counting methods, rounding guidelines, and multi-step calculations from Doctor Marciro's lecture.

Pacific side rule (Sig Figs)

The counting rule used when a decimal point is present, stating that you count significant figures starting from the left (Pacific) side at the first nonzero digit.

Atlantic side rule (Sig Figs)

The counting rule used when a decimal point is absent, stating that you count significant figures starting from the right (Atlantic) side at the first nonzero digit.

Placeholder zero

A zero that is not significant and serves only to maintain the correct magnitude or place value of a number.

Exact numbers

Values obtained by counting discrete objects or by exact definitions (such as $12\,\text{inches}$ in a foot) that possess infinite significant figures.

Bar over a zero

A notation used on numbers with an absent decimal point to show that counting significant figures begins at that specific marked zero.

Exponential part of scientific notation

The $10^x$ multiplier portion of standard scientific notation, which carries infinite significant figures and does not limit calculation precision.

Rounding rule for digits less than five

An old-school rounding rule stating that if the digit to the right of the last significant figure is less than five, the last significant figure is left unchanged.

Rounding rule for digits five or greater

An old-school rounding rule stating that if the digit to the right of the last significant figure is five or greater, the last significant figure is rounded up.

Sig fig rule for multiplication and division

The calculation rule stating that the final answer must be rounded to match the least number of significant figures among the component numbers.

Sig fig rule for addition and subtraction

The calculation rule stating that the final answer must be rounded to match the least number of decimal places (or least precise place value) among the component numbers.

Combination calculation rounding rule

The procedure of following the order of operations, retaining extra digits during intermediate calculation steps, and rounding only once at the final step.

Percent error

A measure of accuracy comparing an experimental value to an accepted literature value, calculated using the absolute difference divided by the accepted value.

Rule for the mean of a dataset

The precision rule requiring that a calculated mean must be rounded to the same number of decimal places as the individual component measurements.

Significant figures in 2,500

Two significant figures, determined by counting from the Atlantic side starting at the first nonzero digit (five) because the decimal point is absent.

Significant figures in 2.500

Four significant figures, determined by counting from the Pacific side starting at the two because the decimal point is present.

Number of feet in a mile

Exactly $5208\,\text{feet}$, which is a defined conversion factor and therefore possesses infinite significant figures.

Magnitude retention in rounding

The requirement to place non-significant zero placeholders when rounding large numbers to avoid changing the scale of the value.

Step one in counting significant figures

Determining whether the decimal point is present (count from the Pacific/left side) or absent (count from the Atlantic/right side).

Step two in counting significant figures

Locating the first nonzero digit (or marked zero) and counting every digit from that point through to the end of the number.

Significant figures in 0.005

One significant figure, found by counting from the Pacific side through leading placeholder zeros to the single nonzero digit (five).

Number of replicates ($n$)

The count of measured items or trials used when dividing to find a mean, which is an exact counted quantity with infinite significant figures.

Scientific notation representation of 5,000 with three sig figs

$5.00 \times 10^3$, which explicitly displays three significant figures while maintaining the overall value.

Doctor Marciro's sig fig shorthand

The abbreviation sf (or a sideways a and sf) used in lecture notes to represent significant figures.

Precision direction

The increase in measurement precision achieved as digits extend further to the right of the decimal point (tenths, hundredths, thousandths).

Weakest link concept in calculations

The principle that a calculated result cannot be more precise or have more significant figures than the least precise component value.

Significant figures in 10 molecules

Infinite significant figures, because discrete items like molecules cannot be measured in fractional amounts.

Intermediate rounding error

An unintended distortion of calculated results caused by prematurely rounding numbers at individual steps instead of waiting until the end.

Experimental value

The measurement value obtained directly during a test or experiment, used in calculating percent error against an accepted standard.

Accepted value

The standard literature value or known theoretical reference value used to calculate percent error.

Significant figures in 700. (with decimal point)

Three significant figures, because the explicitly written decimal point forces counting from the Pacific side.