Base unit-a defined unit of measurement based on an object or event in the physical world Five base units: Temperature Mass Length Time Energy Derived unit-a unit of measurement defined by a combination of base units Volume Density Measurements In science we use the SI Units(International system) for measuring 1
Accuracy : How close to a measured value is to an accepted value. Precision: How close a series of measurements are to one another Measurements Instruments have a certain level of accuracy How did we see this in the lab? To be accurate always estimate another digit after last certain digit. this is called your estimated digit. WHY? We know that this measurement is somewhere between 105 and 106. So our estimated value would be the tenths place Measurement would be around 105.5 ml 2
Measurements 43.0 ml We are g here, so 10th plac 3
Measurements Practice Significant figures are numbers that count or mean something in an experiment. They represent the level of certainty in measurement based on the equipment used. Only measurements have sig figs. Why? Sig figs are all measured numbers plus one estimated digit. When we measure something, we can (and do) always estimate between the smallest marks or increments. The better the marks, the better we can estimate. When reading a measurement, scientists always understand that the last number measured is actually an estimate. 4
Rules for Sig Figs All nonzero numbers (naturals) are always significant (a) 456 (b) 35 (c) 4 (d) 891 (e) 1,345 (f) 12,345 (g) 4.52 Rules for zero: If it is not a natural number then it must follow other rules... Rules for Sig Figs cont. Rules for zero: 1) Zeros between two nonzero numbers are always significant "TRAPPED!" 2) All final zeros to the right of the decimal (and after a nonzero number) are significant "AFTER, AFTER" 3) Placeholder zeros are not significant (all other zeros) 5)Counting numbers and conversion factors have infinite numbers of significant figures 5
Sig Figs Practice State how many sig figs are present in the following numbers 0.00789 56700 7007 13404.40 5000 4501 0.09800 1005000 560 2315 Which numbers were taken from the most precise instrument? Which numbers were taken from the least precise instrument? How do you know? MULTIPLICATION and DIVISION Multiply or divide normally following the order of operations The answer must contain the same number of significant figures as the number with the least significant figures. Round to that number. Example: What is the density of a metal block that has a mass of 34.5 g and a volume of 13 ml? 6
Practice: a. 31.5 * 56 b. 14.8 / 45 c. 100 * 56.7 d. 9870 / 89.0 e. 99.9909 /10.0 ADDITION and SUBTRACTION When adding numbers, align the decimals. The answer must contain the same number of sig figs after the decimal as the number with the least amount of sig figs to the right of the decimal. Why? Round to that number. 7
Practice: a. 31.5 + 56.890 b. 124.8-45 c. 100.00 + 56.7 d. 9870 + 89.03 e. 99.9909-10.0 Scientific Notation Scientific notation is a form of writing numbers that are too large or too small to be written practically using placeholders. It is also used to express numbers that cannot be written in standard notation and still have the correct amount of sig figs. 8
To convert from standard notation to scientific notation... 1. Move the decimal to the right of the first sig fig. 2. Remove all non significant zeroes 3. Write "X 10" beside the number 4. Count how many places the decimal moved and write that number as an exponent above the 10 5. If the original number was a decimal, the exponent is negative 6. If the original number was NOT a decimal, the exponent is positive. Scientific Notation Practice: Put the following numbers in sci. notation a) 0.00000305 b) 102,000,000,000 c) 0.00000678000 d) 45000 e) 609.00 9
Scientific Notation Practice: Put the following numbers in regular notation 2.34 x 10 2 4.5 x 10 5 5.62 x 10 8 3.45 x 10 3 1.2 x 10 6 4 x 10 4 Multiplication and Division of Scientific notation Multiplication: 1. Multiply the coefficients 2. Add the exponents EX: (2.25 x 10 2 )( 1.9 x 10 5 ) Division: 1. Divide the coefficients 2. subtract the exponents (2.25 x 10 2 ) ( 1.9 x 10 5 ) 10
Examples: A. 2.36 x 10 2 * 1.5 x 10 5 B. 5.82 x 10 2 / 3.45 x 10 3 C. 1.29 x 10 6 * 4.00 x 10 4 D. (3.388 x 10 10 )(9.5 x 10 3 ) E. 1.02 x 10 8 / 3.165 x 10 2 F. (4.20 x 10 4 )(4 x 10 4 ) Addition and Subtraction of Scientific notation 1. Make the exponents the same by moving the decimal to the right or to the left. 2. Add (or subtract) the coefficients Example: (5.6 x 10 3 ) + (4.3 x 10 4 ) 11
Examples A. 2.34 x 10 2 + 4.5 x 10 5 B. 5.62 x 10 8 3.45 x 10 3 C. 1.2 x 10 6 + 4 x 10 4 D. 3.388 x 10 10 + 9.5 x 10 3 E. 1.02 x 10 8 3.165 x 10 2 F. 4.20 x 10 4 4 x 10 4 Error - the difference between an experimental value and an accepted value error = experimental value - accepted value Percent error- expresses error as the percentage of the accepted value percent error = error X 100 accepted value 12
Bertha and Skeeter conducted an experiment on the amount of CO 2 produced by three moles of CH 4 and a liter of O 2. They conducted their trials five different times. Below is their data. trials: grams error? % error? 1 129.5 2 124.6 3 128.0 4 127.0 5 120.2 According to their calculations they should have produced 132.2 grams Two kinds of data or observations: Qualitative data: data that is more anecdotal and cannot or is not be measured, describes the qualities of something Example: shiny, blue, soft, viscous, etc. Quantitative data: measurements recorded from experiments 13
Dimensional Analysis Dimensional Analysis is a method of using conversion factors to convert from one unit to another. A conversion factor is a ratio of two factors that equal each other. Ex: one inch = 2.54 cm Example 2: 0.62 miles = 1 km Since both measurements in a conversion factor equal the exact same distance we can put them over each other and they equal one. 0.62 miles 1 km or 1 km 0.62 miles In math anything can be multiplied by one without changing the quantity. Therefore we can multiply by conversion factors to conveniently switch from one unit to another. If I traveled I16.72 miles, how many meters did I go? 14
Practice: A. How many ml in.0034 L? B. How many mg in 93 kg? C. How many meters in 6.5 X 10 4 μm? 15