Scientific Measurement Chpt 3

Units of Measure –general qualitative – describes matter – ex. Rough, shiny, heavy, blue quantitative – measures matter –Must include numbers and units –when measuring, we read as far as the device will allow and estimate one digit farther – ex. 2g, 52cm, 75mL –we must use units when using quantitative descriptions or our numbers won’t make sense –If I tell you our book is 15, you don’t know what I’m talking about. I need to include a unit to describe what we are measuring. So if I were talking about length, I could say 15cm and then you would understand my description

Scientific Notation –a way to write very large and very small numbers that makes them easier to work with every number written in scientific notation has 2 parts –first, a number between 1 and 10 with any number of digits after the decimal point –second, a power of ten To write a number in scientific notation –move the decimal point to the right or left so that only one digit is in front of the decimal point –count the number of places you moved the decimal point, this becomes the power of ten for the second part –if the number you started with was greater than one, your exponent is positive –if the number you started with was less then one, your exponent is negative

scientific notation in calculations without calculators multiplication: multiply the first parts and add exponents division: divide the first parts and subtract the exponents in addition and subtraction: all values must have the same exponents, convert them, then add or subtract the first parts and keep the exponents the same remember to put the final answers in the correct form of scientific notation

Accuracy is how close a measurement is to the true value its like throwing darts, accuracy is how far you are from the bulls-eye the closer they are to the bulls-eye, the more accurate they are Precision is how close a set of values are to each other its like throwing darts, precision is how close your darts are to each other the closer they are to each other, the more precise they are Measurements can be accurate but not precise, precise but not accurate, both accurate and precise, or neither

Accuracy and Precision –General –all measurements are subject to limits and errors, therefore no value obtained in an experiment is exact to reduce the impact of error, scientists always repeat their experiments, measurements and calculations if their results are not consistent, they will try to identify and eliminate the source of error scientists want their results to be accurate and precise Measurements must involve the right equipment the 1st step to cutting down error is choosing the correct equipment different instruments measure different quantities in different units and different calibrations

Percent Error calculations tell how far your experimental value is from the expected or literature value the formula for % error: % error = /your value – literature value/ x 100 literature value

Significant Figures –scientists always report values using significant figures significant figures are decimal places that are used to determine the amount of rounding to be done based on the precision of the instrument used they are all of the digits that are known with certainty and one estimated or uncertain digit –Significant figures are essential to reporting results when measuring, you must read all certain digits and estimate one further this is necessary to assure results are true, the number of significant digits reported depends on the calibration of the instrument used (practice this in lab!) these figures will help you figure out where to round off answers in calculations

Rules for determining significant digits nonzeros are always significant (ex.46.3m) zeros between significant digits are significant (ex. 40.7m) zeros in front of nonzero digits are not significant (ex m) zeros at the end of a number and to the right of the decimal point are significant (ex m) zeros both at the end of a number but to the left of the decimal point are not usually significant (we will consider them not significant unless there is a decimal point after them, ex. 2000m or 2000.m)

Exact values have unlimited significant figures some values have no uncertainty, in other words they have an unlimited number of significant digits count values, numbers that have been determined by counting not measuring conversion factors ignore these when determining the number of significant figures in your calculations Calculators do not identify significant figures when using calculators to perform calculations you must count significant digits to know where to round off your answer

Rules for using significant figures in calculations in multiplication and division: the answer cannot have more significant figures than the least given in the measurement or question, do not round until the end (count sig. digs.) in addition and subtraction: the answer cannot have more decimal places than the least given in the measurement or question, round at the end (count decimal places) if a calculation has both addition/subtraction and multiplication/division: round appropriately after each step significant digits with scientific notation the exponents are count values, look only at the first part of the scientific notation

The SI system scientists worldwide use the same system of measurement (units) this way they can understand each others results and experiments this system is call the Systeme Internationale d’Unites (international system of units) which we abbreviate as SI this system is built on seven base units (we will 4 or 5 of these this year) see table 3.1, page 74 sometimes these base units can be too large or too small for the quantity we want to measure

we use prefixes to modify the units and make them appropriate for the quantity we are measuring these prefixes are based on tens k h da __ d c m, these are the most common Micro = 10 -6, nano = ex. The base unit of length is the meter. If we wanted to measure how far it is from Marion to Myrtle Beach, meters would be rather small. So, we add a prefix in front of meters and make it kilometers which adjusts our measurement to a unit that is appropriate for what we wanted to measure. We could have used meters, but it wouldn’t have been convenient. see table 3.3, page 75 make sure you understand these prefixes and how they relate to the base unit and each other

Converting from One Unit to Another sometimes we need to convert from one unit to another one way to do this, is to use a conversion factor (called factor label method or dimensional analysis) a conversion factor is a ratio that relates the 2 units (the starting unit and the unit we want to convert to) we then write the conversion factor as a fraction set up to cancel the starting unit and end up with the new unit (this is called the factor label system and we use a grid system to set up the problem) ex. If we want to convert 6 hours to minutes, we must first come up with a ratio that relates the two units. 1 hour = 60 minutes. Then, we write the given quantity in a grid in the top left and arrange the conversion factor as a fraction with the correct unit on the bottom to cancel the given units. do practice problems after you understand this, I’ll show you a shortcut

Derived Units some quantities can’t be measured by one of the seven base units alone, in these cases we have to multiply or divide the base units to get a new unit (a combination of the base units) these new units are called derived units ex. Volume, speed and area

Heat is different from temperature temperature is the measure of how hot or cold something is temperature is actually a measurement of the average kinetic energy of the random movement of particles in a substance heat is transferred energy Temperature is expressed using different scales –there are three main temperature scales –Fahrenheit –Celsius –Kelvin –in chemistry, we don’t use the Fahrenheit scale

Kelvin is the SI scale, but Celsius is used often since we have 2 scales that are used in chemistry, we must be able to convert between the 2 scales the equation to convert between the two is T(K) = t(°C)

density – the ratio of mass to volume derived unit (for solid or liquid g/cm3, for gases g/L) D=m/v the density of a substance is the same no matter the size of the sample, therefore we can use density to help identify unknown substances the density of water is approximately 1g/cm3, therefore whatever its mass is in grams the volume in cm3 will me equal to the mass density can also be determined graphically graph the mass vs. volume for different size samples, then take the slope of the line (rise/mass over run/volume) to determine the density