# Making Measurements and Using Numbers The guide to lab calculations.

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Making Measurements and Using Numbers The guide to lab calculations

Not just numbers  Scientists express values that are obtained in the lab. In the lab we use scales, thermometers and graduated cylinders to record mass, temperature and volume. It may seem simple to read the instruments but it is actually more difficult than you think.

Reading Thermometers  Thermometers measure temperature. Key points:  Temperature is read from the bottom to top.  Lines on a thermometer are only so accurate. We as scientist are allowed to estimate between the lines.  The unit on thermometers is Celsius

Estimating Lines  We are allowed to estimate one additional digit to make the reading more significant.  No matter what the last line of reading may be on the thermometer, you may estimate one additional digit (with a few exceptions)

Estimation Tips  When markings go up or down by ones, estimate your measurement to the tenths place  When markings go up or down by tenths, estimate your measurement to the hundreths place  When markings go up or down by 2 ones or 2 tenths, estimate your measurement to that place

Why do we estimate lines?  Some errors or uncertainty always exists in measurements. The measuring instruments place limitations on precision.  When using a device we can be almost certain of a particular number or digit. Simply leaving the estimated digit out would be misleading because we do have some indication of the value’s likely range.

Reading Liquid Volume  Because of certain physical properties, liquids are attracted or repelled from glass surfaces. Water is especially attracted to glass. Due to this attraction a meniscus forms when water is in glass tubing.  Meniscus is the upside down bubble that forms when water is in glass

 When reading glass volumes, the volume is of liquid is read at the bottom of the meniscus.  Not only is the liquid read at the bottom of the meniscus but the last digit of the reading is estimated.  The estimation tips are the same for all measuring devices  No matter the guess you are right. As long as you include the guess in your answer

Water Meniscus

Significant figures  In science, measured values are reported in terms of significant figures.  Significant Figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.

Why Use Sig Figs?  We can only measure as well as our equipment  We cannot make estimates without being precise  Estimating multiple measurements can add up to a lot of error

 Insignificant digits are not reported, ever. Scientist don’t write down all the numbers the calculator displays.  To determine if a value is significant the following rules are applied:

Rule 1  All non-zero numbers are significant.  Examples:  123 L has 3 significant figures (sigfigs)  7.896 m 3 has 4 sig figs  8 meters has 1 sig figs

Rule 2  Zeros appearing between non zero digits are significant.  Examples:  40.7 L has 3 sig figs  87,009 km has 5 sig figs

Rule 3  Zeros appearing in front of all non zero digits are not significant.  Examples  0.095897 m has 5 sig figs  0.0009 kg has 1 sig fig  These zeros are place holders

Rule 4  Zeros at the end of a number AND to the right of a decimal point are significant.  Examples  85.00 g has 4 sig figs  9.000000000 mm has 10 sig figs

Rule 5  Zeros at the end of a number but to the left of a decimal point may or may not be significant. If a zero has not been measured or estimated but is just a placeholder, it is not significant. A decimal point placed after zeros indicates they are significant  Examples  2000 m has only 1 sig fig  2000. M has 4 sig fig (decimal at the end)

When To Apply Sig Fig Rules?  Sig fig rules only apply to situations where a measurement was made by an instrument.  For all other situations, all measurements are exact, and therefore contain an unlimited amount of significant figures. 300 mL = 1 sig fig 300 people = 3 sig figs 300 pennies = 3 sig figs

Calculations with Sig Figs  When multiplying and dividing, limit and round to the the number with the fewest sig figs.  5.4 x 17.2 x 0.0005467 =?

 When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer  142.3 + 12 - 0.61 =?

Working with numbers continued  How many sig figs are in the number 23000000000?  Do we need to write all of the zeros?

Scientific notation  Scientist often deal with very small and very large numbers, which can lead to a lot of confusion about counting zeros.  Scientist notation takes the from of M x 10 n where 1 <M<10 and “n” represents the number of decimal places moved.

 150000 becomes 1.5 x 10 5  43500000 becomes 4.35 x 10 7  0.0034 becomes 3.4 x 10 -3  0.000000000005687 becomes 5.687 x 10 -12 More examples…

Multiplying & Dividing Using Scientific Notation  Ex: (4.58 x 10 5 ) (6.8 x 10 -3 )  Multiply the bases  Add the exponents  Adjust value to correct scientific notation format  Determine sig figs from quantities listed in the original problem

 Ex: (2.8 x 10 -5 ) / (1.673 x 10 -2 )  Divide the bases  Subtract the exponents  Adjust value to correct scientific notation format  Determine sig figs from quantities listed in the original problem

Adding & Subtracting Using Scientific Notation  Ex: (3.52 x 10 6 ) + (5.9 x 10 5 ) – (6.447 x 10 4 )  Convert all quantities so that they all have the same largest exponent  Add or subtract the base numbers  Adjust value to correct scientific notation format  Determine sig figs from quantities listed when all exponents have been adjusted. 

Accuracy vs. Precision  Accuracy is the ability of a tool or technique to measure close to the accepted value of the quantity being measured (how close it is to being right)  Precision is the ability of a tool or technique to measure in a consistent way (how close the measurements are to each other)

Example Problem  A student measured a magnesium strip 3 times and recorded the following measurements: 5.49cm, 5.48cm, 5.50cm The actual length of the strip is 5.98cm. Describe the results in terms of accuracy and precision.

Density  Density is a mass to volume ratio  D = m/vm = Dvv = m/D  Density is an intensive property and will not change regardless of the amount of matter present.  Each substance has its own defined density valueex. H 2 O = 1g/cm 3

How Can Density Be Determined In The Lab?  You must know the mass and volume if you want to experimentally determine the density of a sample of matter  Mass can be found using a scale (g)  Volume can be found by one of two ways:  For regular shaped objects, use a ruler to find l x w x h (measurement will be in cm 3 )  For irregular shaped objects, use water displacement (measurement will be in mL)

 Remember…1cm 3 = 1mL  Water displacement is a process in which an object is submerged in water. The difference between the water level before and after the object is submerged in the water will be the volume of the object

Percent Error… How Wrong Are You?  Once your densities are determined experimentally, you can then compare your lab results to the theoretical value by using the following equation:  % error = (theoretical – experimental) theoretical X 100 Ideally, you would shoot for <5% error in any lab experiment Theoretical values are given by teacher or text

Calculations With Conversions  78.6 mm + 68.350 cm =  55 L + 25 cm 3 =

Calculations With Conversions  The density of cork is.193 g/cm 3. What is the mass in pounds of 7.0 x 10 3 mL of cork? (1 lb = 16 oz), (1 g =.0353 oz)

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