Chapter 2: Measurements and Calculations

Ch 2.1 Scientific Method Steps to the Scientific Method (1) Make observations-- Use your 5 senses to gather information. (2) Propose a hypothesis-- Make an “educated guess” for what is happening. (3) Perform experiments-- This tests your hypothesis. Many experiments are sometimes needed to test a hypothesis. The same experiment must give similar results if the experiment is to be reliable. (4) Make a theory-- This should explain the results of your experiments. Theories may change or be rejected over time because of results from new experiments.

Models: are a part of theory that is an explanation of how phenomena occur and how data or events are related. Qualitative Data: non-numerical data (ex. Green car) Quantitative Data: numerical data (ex. 12 cars)

Ch 2.2 Measurement

Every measurement must have a unit.

Base Units There are 7 base units in SI. A Base unit is a defined unit in a system of measurement that is based on an object SI Base Units Length (l)Meter (m) Mass (m)Kilogram (kg) Time (t)Second (s) Temperature (T)Kelvin (K) Celsius (°C) Amount of Substance (n) Mole (mol) Electric Current (I) Ampere (A) Luminous Intensity (I v ) Candela (cd)

Metric System An easy way to move within the metric system is by moving the decimal point one place for each “step” desired Example: change meters to centimeters Use Prefixes!!! Basic Unit Kilo 1000 Hecto 100 Deka 10 Deci 10 Centi 100 Milli 1000 To convert to a smaller unit, move decimal point to the right or multiply. To convert to a bigger unit, move decimal point to the left or divide.

Metric System centimeters = _________kilometers 500 kilometers = __________meters Basic Unit Kilo 1000 Hecto 100 Deka 10 Deci 10 Centi 100 Milli 1000 To convert to a smaller unit, move decimal point to the right or multiply. To convert to a bigger unit, move decimal point to the left or divide.

Derived Units A unit that is defined by a combination of base units is called a derived unit. Examples are Area, Volume, Density, Molar Mass, Molar Volume, and Energy. The two derived units we will be working with in this chapter are volume and density.

Volume Volume is the space occupied by an object. The derived unit for volume is the cubic centimeter (cm 3 ); used for solid objects. Liters (L) are used to measure the amount of liquid in a container. For the smaller quantities of liquids, volume is measured in milliliters (mL). 1 mL = 1 cm 3

Density Density is a ratio that compares the mass of an object to its volume The units for density: grams per cubic centimeter(g/cm 3 ) for solids grams per milliliter (g/mL) for liquids

The density of an object will determine if it will float or sink in another phase. If an object floats, it is less dense than the other substance. If it sinks, it is more dense. The density of water is 1.0 g/ml.

A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm 3. Calculate the density of aluminum. 2.7 g/cm 3 Example 1 Answer

A conversion factor is a ratio of equivalent values used to express the same quantity in different units.

A conversion factor is always equal to 1. Because a quantity does not change when it is multiplied or divided by 1, conversion factors change the units of a quantity without changing its value. This is also known as dimensional analysis and it will be used a lot throughout the year. The key to doing dimensional analysis is making sure that your units cancel out!

Example 2 Express a mass of grams in milligrams and kilograms Grams to milligrams 1 g = 1000 mg Grams to kilograms 1 kg = 1000 g

Answer 5712 mg kg

Temperature The temperature of an object is a measure of how hot or cold the object is relative to other objects. Temperature scales - scientists use two temperature scales Celsius ( o C) scale was devised by Anders Celsius Freezing point of water – 0 o C Boiling point of water – 100 o C the Kelvin (K) scale was devised by William Thomson and is the SI base unit of temperature On the Kelvin scale water freezes at 273 K and boils at 373 K °C = K K – 273 = °C

Convert the following Celsius temperatures to Kelvin. A. 42 o C Example B. 100 o C C. 68 o C

Ch 2.3 Using Scientific Measurements A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. Precision refers to the degree of agreement among several measurements made in the same manner. Precision refers to the degree of agreement among several measurements made in the same manner. Neither accurate nor precise Precise but not accurate Precise AND accurate

Percent Error Experimental values are measured during an experiment Accepted value = true value Error = (Experimental value - accepted value) When you calculate percent error, you ignore plus and minus signs The lower the % error means lab technique is good.

Significant Figures Scientist indicate the precision of measurements by the number of digits they report - Significant figures or Sig Figs A value of 3.52 g is more precise than a value of 3.5 g.

Rules for Counting Significant Figures in a Measurement Here is how you count the number of sig. figs. in a given measurement: #1 (Non-Zero Rule): All digits 1-9 are significant. *Examples: 2.35 g =_____S.F g = _____ S.F. #2 (Straddle Rule): Zeros between two sig. figs. are significant. *Examples: 205 m =_____S.F m =_____S.F cm =_____S.F. #3 (Righty-Righty Rule): Zeros to the right of a decimal point AND anywhere to the right of a sig. fig. are significant. *Examples: 2.30 sec. =_____S.F sec. =_____S.F km =_____S.F

Rules for Counting Significant Figures in a Measurement #4 (Bar Rule): Any zeros that have a bar placed over them are sig. (This will only be used for zeros that are not already significant because of Rules 2 & 3.) *Examples: 3,000,000 m/s =_____S.F. 20 lbs =____S.F. #5 (Counting Rule): Any time the measurement is determined by simply counting the number of objects, the value has an infinite number of sig. figs. (This also includes any conversion factor involving counting.) *Examples: 15 students =_____S.F. 29 pencils = ____S.F. 7 days/week =____S.F. 60 sec/min =____S.F. 42 ∞ ∞ ∞ ∞

Sig Fig Practice #1 How many significant figures in each of the following? m  5 sig figs kg  4 sig figs 100,890 L  5 sig figs 3.29 x 10 3 s  3 sig figs cm  2 sig figs 3,200,000  2 sig figs

Rules for Significant Figures in Mathematical Operations Addition and Subtraction: use the least number of places after the decimal between all the numbers you are adding or subtracting = =  18.7 (3 sig figs)  18.7 (3 sig figs)

Sig Fig Practice # m m CalculationCalculator says:Answer m 10.2 m g g g 76.3 g 0.02 cm cm cm 2.39 cm L L L709.2 L

Rules for Significant Figures in Mathematical Operations Multiplication and Division: use the least number of sig figs between the numbers you are measuring x 2.0 = 6.38 x 2.0 =  13 (2 sig figs)  13 (2 sig figs)

Sig Fig Practice # m x 7.0 m CalculationCalculator says:Answer m 2 23 m g ÷ 23.7 cm g/cm g/cm cm x cm cm cm m ÷ 3.0 s m/s240 m/s

Scientific Notation Cartoon courtesy of NearingZero.net

Scientific Notation Scientific notation is a way of representing really large or small numbers using powers of 10. *Examples: 5,203,000,000,000 miles = x miles mm = 4.2 x 10 −8 mm Steps for Writing Numbers in Scientific Notation (1) Write down all the sig. figs. (2) Put the decimal point between the first and second digit. (3) Write “x 10”

(4) Count how many places the decimal point has moved from it’s original location. This will be the exponent...either + or −. (5) If the original # was greater than 1, the exponent is +, and if the original # was less than 1, the exponent is -....(In other words, large numbers have + exponents, and small numbers have - exponents.)

477,000,000 miles = _______________miles m = _________________ m 6.31 x 10 9 miles = ___________________ miles 3.88 x 10 −6 kg = __________________ kg Scientific Notation Practice Problems: Write the following measurements in scientific notation or back to their expanded form. Practice Problems: Write the following measurements in scientific notation or back to their expanded form x x 10 −4 6,310,000,

PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION ADDITION AND SUBTRACTION

4 x x 10 6 IF the exponents are the same, we simply add the numbers in front and bring the exponent down unchanged. 7 x 10 6

4 x x 10 6 The same holds true for subtraction in scientific notation. 1 x 10 6

4.00 x x 10 5 If the exponents are NOT the same, we must move a decimal to make them the same.

4.00 x x x x 10 6 Move the decimal on the smaller number! 4.00 x 10 6

A Problem for you… 2.37 x x 10 -4

2.37 x x Solution… x 10 -6

x Solution… x x x 10 -4

MULTIPLYING AND DIVIDING

4.0 x 10 6 X 3.0 x 10 5 Multiply the front factors first. Then add the exponents.

x 3.0 x x = 4.0 x 10 6 Make sure that only one number is in front of the decimal at the end of the problem. 1.2 x 10 12

4.0 x 10 6 ÷ 3.0 x 10 5 Divide the front factors first. Then subtract the exponents.

÷ 3.0 x x x 10 6

Simplify the following scientific notation problems. Example B. A.

Answers B. A.