Data Collection Notes How good are data?

Accuracy and Precision Though the terms are frequently used interchangeably, accuracy and precision are two different things. – Accuracy: How close a measured value is to the true value. – Precision: How close a series of measurements are to each other.

Accurate and precise: The knife thrower is precise (the knives are closely placed to one another) and accurate (the knives are where he wants it).

Neither accurate nor precise: The knife thrower has neither placed the knives close to each other (making it imprecise) nor placed them where he wanted them (making them inaccurate).

Precise, but not accurate: The knife thrower is precise (the knives are closely grouped) but not accurate (they are presumably not where he wanted them).

How can we tell if data are accurate? In order to determine if data are accurate, we must first know what the actual value of the thing being measured is. The accuracy of a measurement is expressed by the measurement’s “percent error”:

Percent Error A high percent error means that the data were not very accurate, while a low percent error means that they were. Example: The mass of a sample of a compound was found to be 45.0 grams. If the actual mass of the compound was 55.0 grams, what is the percent error of this calculation? 18.2%

How can we tell if data are precise? The number of decimal places that are shown in a measured value give us an idea of how precise they are. For example, the measurement “18.0 grams” is assumed to be precise to the nearest 0.1 grams because if it wasn’t, we wouldn’t have gone to the trouble of writing the “.0” at the end of the value. The digits in a measured value that give us this kind of information are referred to as “significant digits” or “significant figures.” Any digit that gives us useful information is said to be significant.

Sig Fig Rules: – Nonzero numbers in measurements are always significant. The number “35 grams” has two significant figures and is precise to the nearest whole gram. – Zeros between nonzero numbers are always significant. The number “202 grams” has three significant figures and is precise to the nearest whole gram. – Zeros to the left of all nonzero digits are never significant. They’re just placeholders. The number “0.02 grams” has one significant figure and is assumed to be precise to the nearest 0.01 gram. This rule is set up so that we get the same number of significant figures whether or not we use scientific notation.

Sig Fig Rules Continued: – Zeros to the right of all nonzero digits are only significant if there’s a decimal place explicitly shown. The number “2.00 grams” has three significant figures and is assumed to be precise to the nearest 0.01 gram. The number “ grams” has two significant figures and is assumed to be precise to the nearest gram. – When using scientific notation, only pay attention to the part of the value before the “x”. The number “2.0 x 10 2 grams” has two significant figures and is precise to the nearest 0.1 x 10 2 grams.

PRACTICE! How many sig figs in each? ,000,000 2

Calculating with Sig Figs When we do calculations using data, we need to make sure that our answers also reflect the value of the data that went into making them.

Calculating with Sig Figs When adding and subtracting, the answer should be rounded to the last significant figure of the least precise value.

PRACTICE! = 344 1, – 17.6 = 1, – 16.2 = =

Calculating with Sig Figs When multiplying and dividing, the answer should have the same number of significant figures as the value with the least number of significant figures grams / mL = 3.29 g/mL – “34.0 grams” has three significant figures and “10.33 mL” has four significant figures. Our answer, then, will be rounded to three significant figures.

PRACTICE! grams x grams = sq grams 854 meters x meters = 5.3 sq meters 220 grams / 16.2 cm 3 = 14 g/cm / 10.01= 14.99