Bell Ringer: Notebook Setup Name on inside front cover We will # each page front & back Start by numbering all you pages to 20 (only 10 sheets of paper)

Bell Ringer: Copy down objective in header Pg11- Express numbers in scientific and standard notation to the correct number of significant figures. Homework: watch math measurement video (will be posted to Edmodo & hollickchemistry.weebly.com) Take notes on page 12

When would we need to use scientific notation? When measurements are REALLY BIG or REALLY SMALL The Earth’s circumference is 4.0075x107 meters OR 4.0075x10 x10 x10 x10 x10 x10 x10 More convenient to shorten using scientific notation

Scientific notation rules notes The coefficient must be greater than or equal to _____ and less than ____.

Scientific notation rules notes Decimal always goes BEHIND the first non-zero digit Count how many times you must move the decimal If the number is BIG the exponent is POSITIVE If the number is SMALL the exponent is NEGATIVE Coefficient Value x 10Exponent

Scientific notation Practice 0.225 L 44,163 g 0.0000091 m

Standard Notation 6.750x102 g 4.35x10-4 L 3.164x108 m

How precise can you be? Significant Figures

What is the difference between the following numbers? 20. 20.0 20.00 Remember, when reading a measurement you can only estimate one place past the smallest increment. 20 30 10 20 21 19 25 20 15

What are significant figures? The digits in a number that tell you the precision of the measurement that generated them 5 6 7 8 5 6 7 8

Instrumentation & Measurment More divisions of measurement the more EXACT we can be. The more decimals the more exact a measurement is

How can we increase accuracy? Increasing the numbers of significant digits! Significant digit- all numbers in a measurement plus an extra for estimation. 6.60 mL 6.63 mL

Why are there significant figures? Equipment can only give you so many decimal places… you cannot be more or less precise than your equipment’s smallest increment. Calculators can give you too many or too few decimal places we need to know when to stop.

Rules for recognizing significant figures Rule #1: Non-zero digits and zeros between non- zero digits are always significant. In other words, non-zero numbers and any zeros sandwiched between them are always significant. 1974 23516 4 sig figs 5 sig figs 2006.8 19806 5 sig figs 5 sig figs

Rule #2: Leading zeros are not significant. In other words, leading zeroes at the beginning of a decimal are not significant. 0.0253 0.001111 0.00000083 3 sig figs 4 sig figs 2 sig figs 2.53 x 10-2 1.111 x 10-3 8.3 x 10-7

Rule #3: Zeros to the right of all non-zero digits are only significant if a decimal point is shown. In other words, trailing zeroes at the end of a number that does not have a decimal point are not significant. 845.10 286.0 4320 5 sig figs 4 sig figs 3 sig figs 83,000,000 100. 3 sig figs 2 sig figs

Rule #4: For values written in scientific notation, the digits in the coefficient are significant. 6.02 x 1023 7.998 x 10-3 4.320 x 103 3 sig figs 4 sig figs 4 sig figs

Rule #5: When multiplying or dividing your final answer has the same amount of significant figures as the lowest given number. 65,400 x 5.0 =

Precision vs. Accuracy Precision: How repeatable is the measurement? Compare your measurement to other measurements you have taken with the same piece of equipment to determine precision. Accuracy: How “correct” is the measurement? Compare your measurement to a known standard to determine accuracy.

Precision vs. Accuracy Let’s draw some bullseyes: Accurate Precise

Precision vs. Accuracy Let’s draw some bullseyes: Accurate & Precise Neither Accurate or Precise

How many “points” do you need to prove Accuracy, you need only 1 “point” Precision, you need many points (at least 3)

Sci Notation in the calculator

Calculations with Sig Figs Example 2: 9.63 x 1012 8.17 x 10-5

Calculations with Sig Figs Example 3: 99,999.99 / 0.001 =

Calculations with Sig Figs Example 4: 3.0 x 4 =