Measurements in Science Units of Measurement Percent Error Sig Figs Density

Measurement Must have a standard = same A standard is an exact quantity people agree to use for comparison. A standard means two people using the same object should get close to the same results.

The English system is very confusing because it has so many different values

Scientists give the English system the thumbs down Scientists needed an exact and uniform system of weights and measurements

The Mistake Two different groups of scientists were working on the calculations to send a probe to Mars. The American team did their calculations in the English standard and the other team did it in the metric system (OOPS!) MARS

This made scientists very upset. It cost the space program 125 million dollars It cost the scientists their time

All scientists must use the same measurement units To measure the properties of matter scientists use the metric system with the following units: Mass – grams (g) Volume – Liters (L) Length – meters (m) Temperature – Celsius (˚C) or Kelvin (K) Time – seconds (s)

Metric Conversions 6000 liters = ________ kl 0.23 g = _________mg k h da UNIT d c m 6000 liters = ________ kl 0.23 g = _________mg 5 hm= ________ cm 9 g = ______ dg

Practice 15hL = _______dL 2.5cm = ________dam 0.05kg = ________g 389cL = ___________mL

A measurement is a quantity that has both a number and a unit. 2.34 g 36.1 mL 16.5 Years Old Measurements are fundamental to the experimental sciences so it is important to be able to make measurements correctly. Always take multiple measurements to ensure a correct answer. Always compare your measurements.

Accuracy and Precision Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured. (closest to TRUE Value) Precision is a measure of how close a series of measurements are to one another. (repeated Value) Accuracy and Precision

Accuracy vs. Precision ACCURATE = CORRECT PRECISE = CONSISTENT

Looking at the measurements (guesses) Which measurement was more ACCURATE? Which group PRECISE in the measurements of Boss’ age?

Accuracy, Precision, and Error How do you evaluate accuracy and precision? (Your thoughts???) Here is an example: How old is my dog? _____ Months (everyone must guess)

44 How old is Boss? Boss is ____ Months old 1. Write down your guess on a piece of paper with your name. 2. Pass them to someone at your table 3.Collect data Boss is ____ Months old 44

Example Mrs. Mathieson’s 5th period class split into 3 groups and each person in the group measured the volume of a 2L Coke. Describe each groups measurements in terms of accuracy and precision. Group A: 1800mL, 1.75L, 1850mL, 1600mL Group B: 1000mL, 2100mL, 2.2L, 1500mL Group C: 2L, 2000mL, 1999L, 2L

How should objects be measured so that you get the most accurate measurement? Significant Figures!!!

Significant Figures relate to the certainty (precision) of a measurement – (If you are buying something that costs $1,000,000 per centimeter how certain (how PRECISE) do you want your measurement to be?) Significant Figures (Sig Figs) = Known + ESTIMATE The significant figures in a measurement include all of the digits that are known (counted), plus a last digit that is estimated.

Counted = KNOWN Measured = ESTIMATED _ (.6 is the estimate) _ (.007 is the estimated) Three differently calibrated meter sticks are used to measure the length of a board. a) A meter stick calibrated in a 1-m interval. b) A meter stick calibrated in 0.1-m intervals. c) A meter stick calibrated in 0.01-m intervals. Measuring How many significant figures are reported in each measurement? Most certainty and greatest PRECISION

Look at the warm up Did any student measure the actual (exact) length of the Mg ribbon? They were all wrong (not exact) so they all had some amount of error in their measurement – right?

Determining Error The experimental value (EV) is the value measured in the lab. (by the student) The accepted value (AV) is the correct value based on reliable references. The error is the difference between the experimental value and the accepted value

% error is used to evaluate how well you made a measurement. Percent Error Percent Error = x 100% EV - AV AV % error is used to evaluate how well you made a measurement. Lower % error = more accurate Higher % error = less accurate Expressing very large numbers, such as the estimated number of stars in a galaxy, is easier if scientific notation is used.

Look at the warm up Calculate the % error of all 4 students Who was more accurate? How can you prove it?

Once sig figs have been measured – now they must be counted Counting sig figs is easy but you must learn the RULES!

Significant Figures RULES Learn these rules: All nonzero digits are significant. 876 Zeros to right of decimal and to right of non zero digit are significant. 692.00 Zeros between 2 nonzero digits are significant. 90,909 90,087.00101 Zeros to the left of a decimal and left of a nonzero digit are not significant. 0.0210 Zeros to the right of a decimal that serve as placeholders before nonzero digits are not significant. 0.0000003109901 Zeros to the left of an understood decimal and to the right of nonzero digits are not significant. 9,340,010,000

Sig Fig Checklist

How many SF are in each? 3,000.21 45.9009 9,090,000 821.000340 124,678 0.001201340 99.100 0. 90101

Math in Science Math is used in science all the time! When doing experiments, math functions are used to determine our outcome of the experiment. Math functions are addition, subtraction, multiplication, division, etc. Biggest issue with Math in Science … How do you round your answer?

Rounding Rules!!! Addition and subtraction, round answer to same number of decimal places as least in problem. Ex. 500.1g + 11.22g = 511.32g = 511.3g (1 dp) (2 dp) (2dp) (1dp) Ex. 455.564m - 50.1m = 405.464m = 405.5m (3dp) (1dp) (3dp) (1dp)

Try these Answer the following, be sure to round your answer correctly. 34.6 + 13 = ______ = 9.02 - 2.9 = ______ = 85.04 + .095 = _____ = 11.0 - 0.044 = ______ = 32.1 + 4.98 = ______ =

Rounding Rules!!! Multiplication and division, round answer to same number of sig as the least in the problem Ex. 500 x 11 = 5,500 = 6000 (1 SF) (2 SF) (2SF) (1SF) Ex. 45/9.0 = 5 = 5.0 both have 2 SFs (1SF) (2SF)

Try these Answer the following, be sure to round your answer correctly. 34.2 x 13 = _____ = 9 x 2 = _____ = 95.0/9 = _____ = 1/4 = _____ = 32/4.0 = _____ =

Density

Density is the relationship of mass to volume Density is the relationship of mass to volume. The amount of matter that is packed into a specific space

M D = V Density Density – an object’s mass per unit volume A physical property Formula: M – mass (g) V – volume (mL) or (cm3) D = M V

Derived Units Combination of base units used in the formula. (g/mL) (g/cm3) Volume of rectangle = length  width  height 1 cm3 = 1 mL D M V D = M V

Lets practice in the lab Using the equipment & object on your table, you and your tablemates calculate the density of that object. (Be sure to measure your object with the correct units) Use the objects identity and actual density, to calculate the % error of your measurements. On a sheet of paper, write your tablemates names, metal identity, your calculated density and you % error

How many of you have every gotten into the tub only to find out you have filled it too high and water flows over the top?

So what is water displacement?

Water Displacement Just like when you got into the tub, the water level had to go up in proportion to the amount of space you were taking up.

Water Displacement Read your graduated cylinder before carefully placing the object in the cylinder…remember to record your unit of measurement. 20 mL

subtract your beginning water level from you ending water level. Water Displacement subtract your beginning water level from you ending water level. 25 mL 20 mL 5 mL Ending Water Level -Beginning Water Level Volume of the object

Practice If 5 quarters were placed in a graduated cylinder with 22mL and the volume changes to 32mL, what is the density of the quarter? (1 quarter = 3g)