Using Scientific Measurements Chapter 2 Section 3

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

Accuracy vs. Precision ___________________ ____________________ _____________________ _______________________

Percent Error ________________is calculated to help determine the validity of your data Percent error= Sometimes the value is ____________, sometimes ___________, so usually the ____________________is used

Reading Instruments For a ___________device, the rule is to estimate ________________________ _____________________of the device. For a digital device, the rule is to __________________________________

Measuring Rules _____

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

Significant Figures _____________________: 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 ___________________ 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 ____________________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

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

Significant Figure: Rules for Calculations Multiplication and Division Rule: In multiplication or division, the result carries the same number of significant figures as the factor with the _______________________________.

Rules for Calculations Addition and Subtraction Rule: In addition or subtraction, the result carries the same number of decimal places as the quantity with the __________________________ It is helpful to draw a line next to the number with the fewest decimal places. This line determines the number of decimal places in the answer.

Rules for Calculations Rules for Rounding: When rounding to the correct number of significant figures, round down if the last (or leftmost) digit dropped is ________________; round up if the last (or leftmost) digit dropped is ___________________.

Round to two significant figures: 5.37 rounds to ____ Rules for Rounding Round to two significant figures: 5.37 rounds to ____ 5.34 rounds to ____ 5.35 rounds to ____ 5.349 rounds to ______ Notice in the last example that only the last (or leftmost) digit being dropped determines in which direction to round—ignore all digits to the right of it.

Exceptions ___________________________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

Scientific Notation, Continued There are 26,800,000,000,000,000,000,000 helium atoms in 1.00 L of helium gas. Express the number in scientific notation. The typical length between a carbon and oxygen atom in a molecule of carbon dioxide is 0.000000116 m. What is the length expressed in scientific notation?

Direct Proportions Two quantities are directly proportional to each other if dividing one by the other gives a ________ 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 ____________is constant _____________ See the graph on the next page

Graph of Inverse Proportionality