Chapter 3 Outline Scientific Measurement Section 3.1 – Measurements and Their Uncertainty A is a quantity that has both a and a . The typically used in the sciences are those of the _________________________________ ___________________________________. In , a given number is written as the product of two numbers: a _______________ and 10 raised to a . In scientific notation, the is always a number equal to or greater than _____ and less than . Sample Problems Write the following numbers in scientific notation: 39400000 2800 0.000567 0.0000002 Write the following numbers in regular notation: 3.22 x 104 2.1 x 10-5 8 x 102 7.90 x 10-6 is a measure of how _________ a measurement comes to the actual or _______ ___________. is a measure of how close a ________ of measurements are to _____________. Error = The is the correct value. The _________________________ is the value measured in the . The is the absolute value of the error divided by the . Percent Error = So in other words, %E =
Sample Problem A block of aluminum has a mass of 147.3g. A student measures the mass of the block as 138.9g. What is the student’s error? What is the percent error? The in a measurement include all the digits that are __________, plus a last digit that is . Rules for Significant Figures Every digit is significant. Ex: 254 or 65.43 Zeros significant figures are significant. Ex: 3005 or 1.083 Zeros (to the left) the significant figures are not significant. Ex: 0.07902 or 0.6932 Zeros (to the right) the significant figures AND after the decimal place are significant. Ex: 20.3200 or 63000 Numbers that can be and _________ ___________________ have an infinite number of significant figures. 370 crayons or 1km = 1000m In general, a answer cannot be more precise than the ____________________ measurement from which it was calculated. Addition and Subtraction When , your answer can only have the same amount of ___________ ___________ as the number with the ___________ _____________ of decimal places. Sample Exercise Calculate the sum of the three measurements. Give the answer to the correct number of significant figures. 12.52 m + 349.0 m + 8.24 m = Practice Exercise Perform each operation. Express your answers to the correct number of significant figures. a. 61.2 m + 9.35 m + 8.6 m = b. 34.61 m – 17.3 m =
When , your answer can only have the same amount of ___________________________ as the number with the amount of significant figures. Sample Exercise Perform the following operations. Give the answers to the correct number of significant figures. 7.55 m x 0.34 m = Practice Exercise Solve each problem and report your answer with the correct amount of significant figures. 2.10 m x 0.70 m = 8432 m / 12.5 = Section 3.1 Assessment 1. How are accuracy and precision evaluated? 2. A technician experimentally determined the boiling point of octane to be 124.1oC. The actual boiling point of octane is 125.7oC. Calculate the error and the percent error. 3. Determine the number of significant figures in each of the following: a. 11 soccer players c. 10800 m b. 0.070020 m d. 5.00 m3 4. Solve each of the following and express your answer with the correct number of significant figures. a. 0.00072 x 1800 = b. 0.912 – 0.047 = c. 54000 x 3500000000 = Section 3.2 – The International System of The International system of Units (SI) is a revised version of the that scientists use around the world. are used to show a very __________ or quantity. For your prefixes it is important to remember the following:
Example of Base Units Example of Prefix Units m cm L mL g kg Write the conversion factors for the following: cm m g kg s ns dL L Some units are a of SI base units. These are called . Volume = length x width x height (m) (m) (m) = Density = mass (kg) = volume (m3) is the amount of that an object contains. The SI unit is . is the force that measures the pull of on a given . The SI unit is . Since is based on , it changes with . stays regardless of location. is a measure of how _______ ___________an object is. (It is the measure of the of an object’s particles) There are 3 temperature scales that are used: . is zero on the ____________ scale. Kelvin temperature is ______________________ to the kinetic energy (speed) of the particles. If the particles are , then the Kelvin temperature is . Since the particles cannot go slower than ____________, then the Kelvin scale does not have any . The following formulas are used to convert between temperatures: K = oC + 273 oC = 5/9(oF – 32)
Convert 1325 dag to megagrams. Sample Problems (Honors) Convert 60 g/mL to kg/dL. Practice Problems (Honors) Convert 90 km/hr to m/s. Convert 78 hg/mL to g/L. Sample Problem (Honors) Convert 20 km2 to cm2. Practice Problems (Honors) Convert 140 dm3 to hm3. Convert 50 m/s2 to km/hr2. Here is a list of other conversion factors that you need to memorize: 1 in. = 1 kg = 1 cm3 = 1 cal = Sample Problem Convert 120 lbs. into kg. Practice Problems Convert 250 cal into joules. Convert 50 cm3 into liters. Convert 25 m into feet.