Significant Digits, Precision, and Accuracy

Vocabulary flashcards covering measurement reliability, significant figure rules, precision vs. accuracy, exact numbers, and calculations involving significant figures.

Significant digits

Scientific measurements that include every certain digit plus only one estimated (uncertain) digit.

Accuracy

How close measured values are to the actual value.

Precision

How closely a series of measurements agree with one another, directly related to the number of significant digits in a measurement.

Repeated Measurements Reliability

An evaluation of measurement precision and accuracy across repeated trials, such as Student C obtaining an average of $10.01\,g$ for a $10.00\,g$ lead block standard, showing both high precision and accuracy.

Significant Figure Rules for Zeroes

Interior zeroes and ending zeroes after a decimal point are significant, whereas leading zeroes are non-significant place-holders.

Ambiguous Zeroes

Ending zeroes before an implied decimal point (such as $4000\,m$) that make uncertainty unclear, requiring scientific notation to accurately establish precision.

Exact numbers

Numbers that have no uncertainty and possess an unlimited number of significant digits.

Categories of exact numbers

1) Numbers from accurately counting discrete objects; 2) Numbers from defined quantities (e.g., $1000\,mm = 1\,m$); 3) Integral numbers that are part of an equation.

Addition and Subtraction Rule for Significant Figures

A rule stating that the precision of the final result is dictated by the most uncertain value (connected to decimal place uncertainty) in the calculation.

Most Uncertain Value in Addition and Subtraction

The quantity with uncertainty at the highest place value (e.g., $-85000.$ with an assumed uncertainty of $\pm 1000$), which dictates the rounding position of the calculated total.

Multiplication and Division Rule for Significant Figures

A rule stating that the final result should have as many significant digits as the term with the fewest significant figures.

Multistep Calculation Rounding Rule

The protocol of carrying unrounded intermediate values through multi-operation calculations and rounding only the final answer to avoid rounding errors.