MEASURING IN SCIENCE Metric System, units, significant figures, rounding, and scientific notation

ENGLISH VS METRIC SYSTEM Dime width is a millimeter Brick mass is a kilogram Jumbo paperclip’s mass is a gram 2.54cm = 1 inch 1.0 liter – 1.06 quart 1.0 pound = 2.2 kilograms

COMMON METRIC UNITS From section 2.1, pages LENGTH, mdistance between point A and B ruler, meter stick VOLUME, Lamount of space an object takes up graduated cylinder, ruler MASS, gamount of matter in an object triple beam balance, electronic balance DENSITY, g/mL amount of mass in a given volume measure mass & volume, D = M / V TEMPERATURE, °C an indirect measure of heat thermometer

BASE VS. DERIVED UNITS What is the difference between a base unit and a derived unit? BASE UNIT is a defined unit based on an object or event in the physical world. It is independent of other units. Examples: meter, liter, newton, coulomb DERIVED UNIT is defined by a combination of base units. Examples: volume = cm x cm x cm, speed = distance/ time, density = mass/volume

METRIC CONVERSIONS DIVIDE BY 10 MULTIPLY BY 10

PRACTICE 25m = ___________mm 2.6cL = ___________L 1500Kg = ______________ g 23.2dam = _____________ dm

PREFIXES

PERCENT ERROR Calculation of percent error is one way to make a distinction between an observed value and a true or literature value. Percent error can be used to describe the accuracy of results of laboratory investigations if a generally accepted (true or literature value) is known. Percent error is always positive. Take the absolute value. % error = [observed value-true/literature value] x 100 true/literature value

PRACTICE In each of the following, show a setup for your calculation. Do any necessary arithmetic below and write your answers in the spaces at the right. 1. The density of mercury is known to be 13.8 g/cm 3. Results of an experiment give that density to be 14.2 g/cm 3. Calculate the percent error.

PRACTICE 2. The volume of a rectangular solid is known to be 556 cm 3. A student takes the following measurements for the dimensions of the rectangular solid:8.34 cm x 6.19 cm x cm a. What volume is calculated for the rectangular solid from these measurements? b. What is the percent error of these results?

ACCURACY AND PRECISION When taking measurements during a lab, you may need to know if your data is reliable. There are two ways to check reliability. Precision:One way is to repeat the measurement several times. A reliable result will give the same measurement time after time. This is how close a set of measurements for a quantity are to each other, but still can be regardless of correctness. Accuracy:This is how close a measurement is to the correct (standard, literature) value for the quantity.

PRACTICE Two students massed the same sample on two different laboratory balances. The results were as follows: Balance A12.11 g g Balance B g g Which balance is more precise? If the mass of the sample is actually 12.1 g, which is more accurate?

SCIENTIFIC NOTATION Scientific notation is a way of writing numbers that makes it easy to handle very large or very small numbers. Imagine having to write all the zeros associated with Avogadro’s Number – 6.02 x ! 602,214,130,000,000,000,000,000

SCIENTIFIC NOTATION To put a number in Scientific Notation If the number is less than one, move the decimal to the right. The exponent is negative and equals the number of places you moved the decimal point  x If the number is greater than one, move the decimal to the left. The exponent is positive  x 10 3

SCIENTIFIC NOTATION To take a number out of Scientific Notation If the exponent is negative, move the decimal point to the left. The number is less than one x  If the exponent is positive, move the decimal point to the right. The number is greater than one x 10 3  1234

DO NOW Go get the 400mL beaker from your lab drawer. Pour out 10mL of green Hendrixium from the back desk. Record the volume as accurately as you can on the paper provided. Now, pour your Hendrixium into the 250mL beaker in your drawer. Record the volume as accurately as you can. Then, pour your volume of Hendrixium into the 50mL beaker on your desk. Record the volume as accurately as you can. Finally, pour your volume of Hendrixium into the 10mL graduated cylinder. Record the volume. Pour out the Hendrixium, clean and the dry the beaker and return it to the counter top. Return to your seat.

MEASURING SIGNIFICANTLY 400mL beaker 250mL beaker 50mL beaker 10mL graduated cylinder Michael Phelps Justin Gatlin

SIGNIFICANT FIGURES  Helps to determine the exactness of measurements. The last place in a number is the inexact number – all others have been measured with certainty.  The lines below are the same length, but have different measurements.  Look at the examples. Which one can have more significant figures?

SIGNIFICANT FIGURES ATLANTIC-PACIFIC RULE This rule divides measurements into two kinds – those with a decimal point and those without. If a decimal point is present in the number, count significant digits from the Pacific side. (If decimal point is present, count from the Pacific side.) If a decimal point is absent, count from the Atlantic side. You should start counting with the first nonzero digit you find. Thereafter, all digits, including zero, are significant.

SIGNIFICANT FIGURES 1. Digits other than zero are always significant. 2. One or more final zeros used after the decimal point are always significant. 3. Zeros between two other significant digits are always significant. 4. Zeros used solely for spacing the decimal point are not significant. The zeros are place holders only.

SIGNIFICANT FIGURES Counting numbers and defined constants or conversions have an infinite amount of significant figures. Use scientific notation to represent accurate measurements such as 7000 g. This has 1 significant digit, but was accurately measured to 4 significant digits. Should be rewritten as x10 3. This indicates 4 significant digits.

PRACTICE Calculate the number of significant figures in the following measurements g _______ m _______ 3. 75,000 km_______ mg _______ 5. 78,621.0 mL _______ m_______

ROUNDING NUMBERS Sometimes you will be asked to round a number to a particular number of significant digits. Rules for Rounding: If the digit to the immediate right of the last significant figure is less than five, do not change the last significant digit  2.53 If the digit to the immediate right of the last significant figure is five or greater, round up the last significant figure  2.54

SIGNIFICANT FIGURES IN CALCULATIONS Measurements that include inherent uncertainty are often used in calculations. In order to keep the appropriate level of uncertainty, simple rules for significant figures have been developed. ADDITION and SUBTRACTION The number of significant figures to the right of the decimal point in the final sum or difference is determined by the lowest number of significant figures to the right of the decimal point in any of the original numbers. MULTIPLICATION and DIVISION The number of significant figures in the final product or quotient is determined by the original number that has the smallest number of significant figures.

SIGNIFICANT FIGURES IN CALCULATIONS cm cm m x m g g cm cm