Unit 1 Part 2: Measurement Mr. Gates Chemistry

Measurement Measurement is a quantitative description of both a number and a unit. Ex. 6 feet and 2 inches

Standards There needs to be standards in order for units to work. The King’s foot.

Accuracy vs. Precision Accuracy describes how close a measurement is to the accepted value Precision describes how close a measurement is to other measurements taken.

Percent Error Percent Error expresses the accuracy of a measurement %𝐸𝑟𝑟𝑜𝑟= (Actual value) –(Theoretical value) Theoretical value x 100 Practice: If a student weighs a sack of potatoes to be 31.5Ibs, but the label on the sack says it is 32.3Ibs, what is the percent error?

Significant Figures All numbers in a measurement that can be known precisely plus one additional number that is estimated. Digits in a measurement that indicate the precision of an instrument used to take a measurement.

Examples (going for a walk) 3 miles (3 estimated) 1.9 miles (9 estimated) 1.91 miles (1 estimated) 1.918 miles (8 estimated)

Which Figures are Significant? All nonzero digits are significant Ex. 5.3 has two significant figures Zeroes appearing in front (to the left) of a nonzero digit are NOT significant Ex. 0.0275 has three significant figures Zeroes appearing in between two nonzero digits are ALWAYS significant Ex. 2.054 has four significant figures Zeroes appearing to the right of a nonzero number and after the decimal place are significant. Ex. 32.810 has five significant figures Zeroes to the right of nonzero digits and to the left of a decimal place are ambiguous. Ex. 300 has ?? … it depends

Ambiguous Numbers??? 200 miles 200 miles 200. miles 200.0 miles

Practice How many significant figures are in the following numbers? .0891 109.3 6.0 0.0005 1.089 7.0020 .08340

Rules for Rounding If the number to the right of the last significant figure is from 0-4, round down. If the number to the right of the last significant figure is from 5-9, round up. Examples: 26.819 rounded to three significant figures is 26.8 Rounded to four significant figures is 26.82 Practice: 0.01037 Rounded to three significant figures? Rounded to two significant figures?

Practice Round the number 34.1050 to: 2 sig figs 5 sig figs 4 sig figs 34.11 3 sig figs 34.1 Round the number 0.0539801 to: 2 sig figs 0.054 5 sig figs 0.053980 4 sig figs 0.05398 3 sig figs 0.0540

Exceptions that Make the Rule There is an UNLIMITED amount of sig figs in two circumstances. Counted numbers 23 students in class (can’t have a fraction of a person) Exact/defined quantities 12 inches in a foot Like 12.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000… (catching my breath)…000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000…. To infinity and beyond zeroes

Sig Figs w/ Calculations Addition or Subtraction The answer can have no more decimal places than the number with the least decimal places in the calculation. Ex. 4.56-1.2= 3.36, but with proper sig figs the answer is… =3.4 Ex. 9.64+1.751= 11.391, but with proper sig figs the answer is… = 11.39

Sig Figs w/ Calculations Multiplication and Division The answer can have no more sig figs than the number with the least amount of sig figs in the calculation. Ex. 1.24 x 2.6 = 3.224, but with proper sig figs the answer is... = 3.2 Ex. 5.11 x 6.551 = 33.47561, but with proper sig figs the answer is… = 33.5

Scientific Notation Scientific notation is a number written as the product of two numbers. Follows the following format: M x 10N M is some number between 1 and 10 N is the amount of times the decimal places had to be moved. N ≠ decimals

Putting #’s in Sci. Notation Every time the decimal place is moved the exponent must move too. M x 10N If the decimal moves  then the exponent goes down If the decimal moves  then the exponent goes up

In and Out Put into scientific notation: 0.0000361 9,840,000,000 Take out of scientific notation: 3.65 x 107 2.49 x 10-4

Sig Figs and Sci. Notation All of the numbers in proper scientific notation are significant… No ambiguous numbers!!! 2000 is 2.00 x 103 with three sig figs.

Addition/Subtraction in Sci. Notation Adding and Subtracting: Exponents must be the same!!! EX: 5.1 x 105 + 6.07 x 105 11.17 x 105 (not correct sig figs) 11.2 x 105 (not correct sci not.) 1.12 x 106

Multiplying/Dividing in Sci. Notation Multiplying and Dividing: EX: 7.2 x 102 x 4.2 x 103 30.24 x 105 (not correct sig figs) 30. x 105 (not correct sci. not.) 3.0 x 106

International System of Measurement Internationally used system of measurement known as the “Metric System”

Benefits of Using the Metric System Scientist all over the world use this system. They can share and understand each other’s work. Based on multiples of ten. Makes for easier conversions.

SI Base units

Volume The amount of space an object takes up. Base unit is cm3

Mass The amount of matter in an object. Base unit is the kg because the gram is too small.

Weight The pull gravity has on the mass of an object.

Fluid Volume When dealing with a fluid (gas or liquid) the most commonly used unit is the liter (L) 1ml = 1cm3

SI Prefixes

Dimensional Analysis Method of converting from one unit to another of equal value using conversion factors.

Conversion Factors These are fractions that are equal to one because the top is equal to the bottom despite the differing units. Multiplying anything by one will not change the number. Conversion factors spawn from two numbers that are equal to each other. Ex. 100cm = 1m 100𝑐𝑚 1𝑚 or 1𝑚 100𝑐𝑚

Using Dimensional Analysis How many mg are in 1.32kg? =1320000𝑚𝑔 How many seconds are in your lifetime? How many cases of pop will you drink in your lifetime? 1.32kg 1000g 1000mg 1kg 1g

Converting Complex Units What is 19 in2 in ft2?