HOW DO WE READ OUR MEASUREMENTS IN SCIENCE? Significant figures: all numbers in a measurement that are definitely correct plus one estimated one. SPECIAL NOTE: All measurements must include an estimated place even if it a zero

Measuring  Volume- mL, L  Temperature- C, F, K  Mass- g

Reading the Meniscus Always read volume from the bottom of the meniscus. The meniscus is the curved surface of a liquid in a narrow cylindrical container.

Try to avoid parallax errors Parallax errors arise when a meniscus or needle is viewed from an angle rather than from straight-on at eye level. Correct : Viewing the meniscus at eye level Incorrect : viewing the meniscus from an angle

Graduated Cylinders The glass cylinder has etched marks to indicate volumes in mL or L.

Measuring Volume  Determine the volume contained in a graduated cylinder by reading the bottom of the meniscus at eye level.  Read the volume using all certain digits and one uncertain digit.  Certain digits are determined from the calibration marks on the cylinder.  The uncertain digit (the last digit of the reading) is estimated.

Use the graduations to find all certain digits There are two unlabeled graduations below the meniscus, and each graduation represents 1 mL, so the certain digits of the reading are… 52 mL.

Estimate the uncertain digit and take a reading The meniscus is about eight tenths of the way to the next graduation, so the final digit in the reading is. The volume in the graduated cylinder is 0.8 mL 52.8 mL.

10 mL Graduate What is the volume of liquid in the graduate? _. _ _ mL 6 26

25mL graduated cylinder What is the volume of liquid in the graduate? _ _. _ mL 115

100mL graduated cylinder What is the volume of liquid in the graduate? _ _. _ mL 52 7

Self Test Examine the meniscus below and determine the volume of liquid contained in the graduated cylinder. The cylinder contains: _ _. _ mL 760

READING A BURETTE Burette are read the same way as a graduated cylinder except the volume value increases as you go down. What is the value on the burette?

The Thermometer o Determine the temperature by reading the scale on the thermometer at eye level. o Certain digits are determined from the calibration marks on the thermometer. o The uncertain digit (the last digit of the reading) is estimated. o On most thermometers encountered in a general chemistry lab, the tenths place is the uncertain digit.

Reading the Thermometer Determine the readings as shown below on Celsius thermometers: _ _. _  C

Mass and Significant Figures o Determine the mass by reading the riders on the beams at eye level. o Read the mass by using all certain digits and one uncertain digit. o On our balances, the hundreds place is uncertain.

Determining Mass 1. Place object on pan 2. Move riders along beam, starting with the largest, until the pointer is at the zero mark

Check to see that the balance scale is at zero

Read Mass _ _ _. _ _ _ 114? ? ?

Read Mass More Closely _ _ _. _ _ _

HOW DO YOU COUNT SIGNIFICANT FIGURES IN A NUMBER? Rules to use – Digits other than zero are always significant (72) – One or more final zeroes used after the decimal point are always significant (3.100) – Zeroes between other significant digits are always significant ( ) – Zeroes as place holders are never significant ( only 2 is significant)

HOW MANY SIGNIFICANT FIGURES IN EACH NUMBER? 9.00 – Three significant figures 1000 – 1 significant figure – 4 significant figures – 2 significant figures

TRICK FOR COUNTING SIGNIFICANT FIGURES 1.Zeroes at the beginning are never significant 2.Zeroes in the middle are always significant 3.Zeroes at the end are significant if there is a decimal point

TRICKS FOR COUNTING SIGNIFICANT FIGURES Pacific/Atlantic Method When using this method start counting from the first non-zero digit If a decimal point is P resent count from the Pacific Ocean side = 5 sig fig If a decimal point is A bsent count from the Atlantic Ocean side = 2 sig figs

Try these: How many significant figures in the following: – 4 sig figs – 4 sig figs 1000 – 1 sig fig – 2 sig figs

HOW DO WE ROUND OFF USING SIGNIFICANT FIGURES?  Multiplication and Division  Round the answer to the same number of significant figures as the least number in the measurement

HOW DO WE ROUND OFF USING SIGNIFICANT FIGURES? Solve and round off to the correct significant figures 78.7/3.0 = Rounded correctly = 26 Why? 78.7 =3 sig fig 3.0 = 2 sig fig Answer has to have two sig fig

Try the following 1.2 X 1.2 X 1.2 = = /3.000 = = 0.667

HOW DO WE ROUND OFF USING SIGNIFICANT FIGURES? AAddition and Subtraction TThe answer should be rounded to the same number of decimal places as the least number in the problem UUse the line method

Try the following = 518.7

Try these Answer: 54.4

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 lb x 3.23 ft lb·ft 5870 lb·ft g ÷ 2.87 mL g/mL2.96 g/mL

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 lb lb lb lb mL mL 0.16 mL mL

In science, we deal with some very LARGE numbers: 1 mole = In science, we deal with some very SMALL numbers: Mass of an electron = kg Scientific Notation

Imagine the difficulty of calculating the mass of 1 mole of electrons! kg x x ???????????????????????????????????

Scientific Notation Scientific Notation –simplified way of expressing very large or very small numbers Form : M X 10 N M= a number between 1 and N= # of Places you move the decimal point to create M

Step #1: Insert an understood decimal point. Step #2: Decide where the decimal must end up so that one number is to its left up so that one number is to its left Step #3: Count how many places you bounce the decimal point the decimal point Step #4: Re-write in the form M x 10 n

2.5 x 10 9 The exponent is the number of places we moved the decimal.

Step #2: Decide where the decimal must end up so that one number is to its left up so that one number is to its left Step #3: Count how many places you bounce the decimal point the decimal point Step #4: Re-write in the form M x 10 n 12345

5.79 x The exponent is negative because the number we started with was less than 1.

Change the following to Proper Scientific Notation X X SPECIAL NOTE: If you start with a number less then one your exponent is negative(-)

Using a Scientific Calculator with Scientific Notation How do you change a number into scientific notation using a scientific calculator ? Enter the number Change to SCI mode Press enter twice to get the answer 5 X 10 7

Using a Scientific Calculator with Scientific Notation How do you put a number into a scientific calculator written in scientific notation? Put 4.8 x 10 6 into your calculator. Press 4.8 EE and 6

USING SCIENTIFIC NOTATION IN MATHEMATICAL OPERATIONS Example: 6.02 X * 1.5 X Place the first number into the calculator 2.Press operation (X in this example) 3.Put the next number in 4.press = 5.Round off your answer to the correct significant figures (Only count the number in the M term to determine the least amount x 10 17

PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION DIVISION AND MULTIPLICATION

Try the following 2.24 x10 3 * 2.0 x10 5 Answer 4.5 x x X10 8 Answer = 4.5 x 10 -5