Scientific Measurement Chapter 3

Not just numbers Scientists express values that are obtained in the lab. In the lab we use balances, thermometers, and graduated cylinders to record mass, temperature, and volume. In 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 scientists are allowed to estimate between the lines. The unit of thermometers is Celcius

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 measuring device being used, you may estimate one additional digit.

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 hundreds 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 so indication of the value’s likely range.

Reading Liquid Volume Because of physical properties, liquids are attracted or repelled from glass surfaces. Water is especially attracted to glass. Due to this attraction, a meniscus forms. Meniscus is the upside down bubble that forms when water is in glass. When reading glass volumes, the volume is read at the bottom of the meniscus.

Reading Liquid Volumes Cont. The last digit of the reading is estimated. The estimating tips are the same for all measuring devices.

Electronic Balances Record all of the digits from the balance.

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 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 may be recorded if they act as placeholders Scientists 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 m 3 has 4 sig figs 8 meters has 1 sig fig

Practice 1 Determine how many sig figs are in the following numbers: 885 mL 4,589,452 Km 96 g

Rule 2 Zeroes appearing between non zero digits are significant. Example: 40.7 L has 3 sig figs 87,008 km has 5 sig figs

Practice 2 Determine how many sig figs are in the following numbers: 305 sec 200,015 m 908,066 molecules

Rule 3 Zeros appearing in front of all non zero digits are not significant These zeros are placeholders Examples: m has 5 sig figs kg has 1 sig fig

Practice 3 Determine how many sig figs are in the following numbers: atm mm psi

Rule 4 Zeros at the end of the number AND to the right of the decimal point are significant Examples: g has 5 sig figs mm has 10 sig figs L has 4 sig figs

Practice 4 Determine how many sig figs are in the following numbers: cm kg molecules

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 m has 4 sig figs (note the decimal at the end)

Practice 5 Determine how many sig figs are in the following numbers: 800 g 800. g Hz

Why do insignificant figures need to sometimes be recorded? Insignificant figures may still be recorded if they act as placeholders to keep the value of how large or small something is credible. 5000m only has 1 sig fig but we still need to keep 3 zeros as placeholders

Cumulative Practice 1 Determine how many sig figs are in the following numbers: 385 sec2,000,000 J 980,510 ft80019 cal 6.0 mm in L 100,000. yd mL

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 sig figs. 300mL = 1 sig fig 300 people = 3 sig figs 300 pennies = 3 sig figs

Cumulative Practice 2 Determine how many sig figs are in the following numbers: 400 lambs 400 mg of sugar lbs 80 bananas

Rounding with Sig Figs Round each of the following calculations to 3 sig figs: ~ ~ ~ ~ Look at the number following the 3 rd sig fig to determine rounding If the number is ≥ 5, round 3 rd sig fig up If the number is < 5, keep 3 rd sig fig the same

Calculations with Sig Figs When multiplying and dividing, limit and round to the number with the fewest sig figs. 5.4 x 17.2 x = ÷2.00 x =

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 = =

Scientific Notation Scientists often deal with very small and very large numbers, which can lead to a lot of confusion about counting zeros. Scientific notation takes the form: M x 10 n where n represents the number of decimal places moved

How are Sig Figs applied to numbers in Scientific Notation? M x 10 n All numbers included in the “M” factor are ALWAYS significant All numbers included in “n” are NEVER significant

becomes 1.5 x becomes 4.35 x becomes 3.4 x becomes x A positive exponent means number greater than one. A negative exponent means a number less than one.

Scientific Notation Practice Write the following in scientific notation or in standard form, given the following: x x 10-2

Multiplying & Dividing Using Scientific Notation Ex: (4.58 x 10 5 ) (6.8 x ) Multiply the bases 4.58 x 6.8 = Add the exponents = 10 2 Adjust value to correct scientific notation format x 10 2 = x 10 3 Determine sig figs from quantities listed in the original problem 3.1 x 10 3

Ex: (2.8 x )/(3.673 x ) Divide the bases 2.8/3.673 = Subtract the exponents – = Adjust value to correct scientific notation format x = x Determine sig figs from quantities listed in the original problem 7.6 x 10 -4

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 (3.52 x 10 6 ) + (.59 x 10 6 ) – ( x 10 6 ) Add or subtract the base numbers = x 10 6 Adjust value to correct scientific notation format: x 10 6 Determine sig figs from quantities listed when all exponents have been adjusted 4.05 x 10 6

Practice Calculations with Scientific Notation (7.36 x 10 2 ) + (2.9 x )= (3 x 10 2 ) x (2.9 x ) = (1.20 x 10 2 ) / (5.000 x 10 5 ) =

Accuracy vs. Precision Accuracy- is how close a measurement comes to the actual or true value of what is being measured Precision- is a measurement of how close a series of measurements are to one another

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

Density Density is a mass to volume ratio D=m/v m=D*v v= m/D Density is a intensive property and will not change regardless of the amount of matter present. Each substance has its own defined density value: Ex: water= 1 g/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 Mass can be found using a balance (g) Volume can be found in 2 ways: For regular shaped objects, use a ruler to find the length x width x height (cm 3 ) For irregular shaped objects, use water displacement (mL)

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 inn the water will be the volume of the object. 1cm 3 = 1 mL

Example Problems A sample of metal has a mass of g and a volume of 45.0 cm3. What is the density of this metal? What is the volume of a piece of zinc with a mass of 25.69g? D zn = 7.14 g/mL

The water level in a graduated cylinder stands at 13.5mL before copper sample is lowered into the cylinder. The water level then rises to 19.8 mL after the sample is submerged. What is the mass of this sample? D Cu = 8.92 g/cm 3

Percent Error…. How Wrong Are You?

Remember…. Theoretical values are definitive. These values are given by the teacher or can be found in a published source (textbook). Experimental results are always found in the lab