CSSI PGCC Barbara A. Gage Measurement CSSI PGCC Barbara A. Gage

CSSI PGCC Barbara A. Gage Measurement Determined magnitude of a property Based on a standard (string…) Must have a unit (which is based on the standard) Number of digits in a measurement depends on the device used CSSI PGCC Barbara A. Gage

CSSI PGCC Barbara A. Gage Height, Width, Depth…? CSSI PGCC Barbara A. Gage

Significant Figures When making a measurement you must record all digits you are sure of and one that is a reasonable estimate (regardless of where the decimal place falls) The object below is 4.86 cm. You can be certain of the 4 and 8. The 6 is an estimate and can vary +/- 1 between measurements. CHM 1010 PGCC Barbara A. Gage

CSSI PGCC Barbara A. Gage Significant figures The graduated cylinder at the right contains 38.34 mL of liquid. It is assumed that you can visually divide the space between lines into ten parts. CSSI PGCC Barbara A. Gage

CSSI PGCC Barbara A. Gage Significant Figures When you encounter a measurement assume that all non-zero digits or zeros between other digits are significant. 23.789 dm 5 sig figs 2.04 gal 3 sig figs 52 kg 2 sig figs CSSI PGCC Barbara A. Gage

CSSI PGCC Barbara A. Gage Significant Figures Zeros may serve as actual measured values or place holders in estimated measurements. Place holder zeros are NOT significant because they are really not measured values. Place holder zeros can be removed by expressing the number in scientific notation. 1,000,000 = 1 x 106 0.000045 = 4.5 x 10-5 CSSI PGCC Barbara A. Gage

CSSI PGCC Barbara A. Gage Significant Figures 120,000 2 significant figures This is an estimate that can be written as 1.2 x 105. 0.0040500 5 significant figures The zeros before and immediately after the decimal point can be eliminated using scientific notation. The last zeros remain because they are actual measurements. 4.0500 x 10-3 CSSI PGCC Barbara A. Gage

Significant Figures –Addition and Subtraction When you are adding and subtracting numbers you only count the columns where you are sure of all the values in that column. CSSI PGCC Barbara A. Gage

Significant Figures –Multiplication and Division When multiplying or dividing two or more values, the answer should contain the number of digits in the value with the least number of significant figures. 0.003570 4 sig figs X 23.4 3 sig figs 0.083538 5 sig figs (calculator answer) You can only trust the answer to 3 sig figs so the correct answer is 8.35 x 10-2. CSSI PGCC Barbara A. Gage

CSSI PGCC Barbara A. Gage Measurement Systems Everyday measurements in the USA are generally made using the English system. The scientific community and most other countries use the metric system. CSSI PGCC Barbara A. Gage

CSSI PGCC Barbara A. Gage Units English System Metric System Length inch, foot, yard, mile meter (or metre) (m) Volume teaspoon, cup, gallon liter (or litre) (L) Mass ounce, pound, ton gram (g) The units in the English system do not have a common conversion factor. 12 in = 1 ft 3 ft = 1 yd 1760 yd = 1 mi The units in the metric system have a common factor which is 10. The metric system uses a common base unit and prefixes to change the size of the unit. CSSI PGCC Barbara A. Gage

CSSI PGCC Barbara A. Gage Metric Prefixes CSSI PGCC Barbara A. Gage

Converting Measurements Often it is necessary to convert a measurement made in one unit to another unit. ex. 2.45 cm = ? m In the metric system you can just shift the decimal point or set up a conversion factor. 2.45 cm = 0.0245 m CSSI PGCC Barbara A. Gage

Converting Measurements Using a conversion factor: 100 cm = 1 m 100 cm or 1m both ratios = 1 1 m 100 cm CSSI PGCC Barbara A. Gage

Converting Measurements If Baltimore is 35 miles away, how far is it in km? Using a conversion factor: 1.61 km = 1 mi CSSI PGCC Barbara A. Gage

Converting Measurements How many mL are in 0.875 gal? 1.06 qt = 1 L 4 qt = 1 gal CSSI PGCC Barbara A. Gage

CSSI PGCC Barbara A. Gage Problem… A gas particle has a velocity of 752 m/s. What is its velocity in mi/hr? 1.61 km = 1 mi CSSI PGCC Barbara A. Gage

CSSI PGCC Barbara A. Gage Problem… A synthesis process requires 6.2 fl. oz. of activator for every 2.5 tons of starting material. What is the concentration of activator in the final product in mL/kg? 1 fl oz = 29.6 mL 2000 lb = 1 ton 2.20 lb = 1 kg CSSI PGCC Barbara A. Gage

Accuracy and Precision Accuracy = how close a result comes to the true value Precision = reproducibility of a measurement CSSI PGCC Barbara A. Gage

Precision and Accuracy Consider 3 persons shooting darts at a target… “a” is precise but not accurate “b” is accurate and precise “c” is not precise or accurate CSSI PGCC Barbara A. Gage

Accuracy and Precision Measurements of the same object made by three students; actual value = 15.71 cm Student 1 Student 2 Student 3 14.72 cm 15.80 cm 15.72 cm 14.71 14.71 15.71 14.72 13.25 15.82 14.82 14.96 15.73 14.71 12.81 15.71 Precise not accurate Not accurate or precise Accurate and precise CSSI PGCC Barbara A. Gage

CSSI PGCC Barbara A. Gage Density Property derived from two measurements, mass and volume Density = Mass/Volume Will have a unit that contains both mass and volume such as g/cm3, lb/gal, kg/L Does not depend on the size of the sample CSSI PGCC Barbara A. Gage

CSSI PGCC Barbara A. Gage Density What is the density of a sample of metal that has a mass of 34.58 g and when placed in 15.0 mL of water causes the level to rise to 22.4 mL? CSSI PGCC Barbara A. Gage

CHM 1010 PGCC Barbara A. Gage