Precision

Learning Objectives Define precision and distinguish it from accuracy. Determine the number of significant figures in a given measurement. Apply the rules of precision for adding and subtracting measurements. Apply the rules of precision for multiplying and dividing measurements. Calculate the greatest possible error (GPE) for a given measurement. Express a measurement's range using tolerance notation (e.g., x ± GPE). Ever measured a piece of wood for a project, cut it, and found it was just a tiny bit too short? 📏 Let's explore why that 'tiny bit' matters! This tutorial introduces the concept of precision, which is all about the level of detail in a measurement. You will learn how to handle calculations with measured numbers so that your answers aren&#...

TermDefinitionExample PrecisionA measure of how close a series of measurements of the same quantity are to one another. It reflects the level of detail of the measurement, indicated by the number of decimal places or significant figures.Measuring a pencil three times and getting 15.21 cm, 15.22 cm, and 15.21 cm is highly precise. A measurement of 15.2 cm is less precise than 15.21 cm. AccuracyA measure of how close a measurement is to the true or accepted value. A measurement can be precise without being accurate.If the true length of a pencil is 16.00 cm, the precise measurements of 15.21 cm and 15.22 cm are not accurate. Significant Figures (Significant Digits)The digits in a number that are reliable and contribute to its precision. This includes all non-zero digits, zeros between non-z...

Addition & Subtraction Precision Rule Round the result to the same number of decimal places as the measurement with the *least* number of decimal places. When adding or subtracting measurements, the precision of the result is limited by the least precise measurement. For example, you can't get an answer precise to the hundredths place if one of your starting numbers was only precise to the tenths place. Multiplication & Division Precision Rule Round the result to the same number of significant figures as the measurement with the *least* number of significant figures. When multiplying or dividing, the number of reliable digits in your answer is limited by the measurement with the fewest reliable digits (significant figures). Greatest Possible Error (GPE) Form...