Using Scientific Measurements Section 2.3

Accuracy vs. Precision Accuracy: the closeness of measurements to the correct or accepted value of the quantity measured Precision: the closeness of a set of measurements of the same quantity made in the same way

Accuracy vs. Precision Accurate and precise Precise, not accurate Accurate, not precise Not accurate nor precise

Percent Error Percent error is calculated to help determine the validity of your data Percent error Sometimes the value is positive, sometimes negative, so usually the absolute value is used

Error in Measurement There is error or uncertainty in any measurement The measuring instruments themselves place limitations on precision There are set rules to using measuring instruments

Reading Instruments For a non-digital device, the rule is to estimate one more digit past the printed scale on the device For a digital device, the rule is to report the exact number of digits displayed

Measuring Rules

Digital Device You can report all the digits displayed which is 12.58 g.

Significant Figures Sig fig: any digit in a measurement that is known with certainty This includes any estimated digit from a non-digital scale There is a system for determining the number of sig figs you are given a measured quantity

Use the Map and the Rules

Rule 1 If a decimal is present in the measured quantity, start from the Pacific Ocean side of the number Move across the number until you get to the first nonzero digit Count it and all the rest Example: 0.00234 m has 3 sig figs

Rule 2 If a decimal is absent, start from the Atlantic Ocean side of the number Move across the number until you get to the first nonzero digit Count it and all the rest Example: 55,240 g has 4 sig figs

Alternate Method There is a set of rules on page 47 in your book You can use either method and get the same results

Rounding Rules Sometimes you will have to round your calculated value to the correct number of sig figs If the digit following the last digit to be kept is 5 or greater, then increase the last digit by 1 If the digit is less than 5, the the last digit should remain the same You may have to use zeros as place-holders

Practice: How many sig figs? 3440. cm 910 m 0.04604 L 0.0067000 kg 3 4 2 4 5

Operations and Sig Figs When multiplying or dividing: Your result can only be as accurate as the measured value with the least number of significant figures (round to reflect this) When adding or subtracting: Your result can only have as many decimal places reported as the measured value with the least number of decimal places

Exceptions Conversion factors or other constants are not considered for significant figure calculations Exact counted numbers are not considered for significant figure calculations

Scientific Notation Numbers are written in the form of M x 10n where 1 ≤ M >10 and n is a whole number Scientific notation is used to exactly show the number of sig figs It is also used to easily calculate very large or very small numbers

Rules for Scientific Notation Determine M by moving the decimal point in the original number to the left or right so that only one nonzero digit remains to the left of the decimal point Determine n by counting the number of places you moved the decimal point If you moved it to the left, n is positive; to the right, n is negative

Direct Proportions Two quantities are directly proportional to each other if dividing one by the other gives a constant value or See the next page for a graph showing this type of relationship

Graph of Direct Proportionality

Inverse Proportions Two quantities are inversely proportional to each other if their product is constant k = xy See the graph on the next page

Graph of Inverse Proportionality

Use of a Comparison of Graphs