MEASUREMENTS

Scientific method – process - logical approach to solving problems Scientific method – process - logical approach to solving problems

SCIENTIFIC METHOD Hypothesis – a testable statement Hypothesis – a testable statement Theory – broad generalization that is supported by facts and data Theory – broad generalization that is supported by facts and data Quantitative data – relates to numerical information Quantitative data – relates to numerical information Qualitative data – non-numerical or descriptive Qualitative data – non-numerical or descriptive

WHAT DO LIBERIA, MYANMAR, AND THE UNITED STATES HAVE IN COMMON?

THE METRIC SYSTEM… A Little History When did the Metric System first originate? The Metric system became compulsory in France on Dec. 10, Japan made it official in 1868 and Russia in England was the last European country to adopt the metric system beginning in 1965.

MODIFIED METRIC SYSTEM The International System of Units

METRIC SYSTEM  We use the metric system when we measure quantities in the lab.  To avoid writing really long numbers, we use prefixes.

PREFIXES USED WITH THE METRIC SYSTEM

MEASURED NUMBERS Measured numbers are the numbers obtained when you measure a quantity. Measured numbers are the numbers obtained when you measure a quantity. Some are read digitally and some are estimated from a mark Some are read digitally and some are estimated from a mark

TO WRITE A MEASURED NUMBER Observe the numerical value of the marked lines Observe the numerical value of the marked lines Estimate value of number between marks Estimate value of number between marks The estimated number is the final number in your measured number The estimated number is the final number in your measured number

TO WRITE A MEASURED NUMBER  Different amount of lines give different significant values.  The last number is estimated.

CONVERSION FACTORS Conversion factor – a ratio derived from the equality between two different units. The ratio is equal to 1. Dimensional analysis – a math technique that allows you to use units to solve problems involving measurements.

CONVERSION FACTORS 1 inch = 2.54 centimeters ounces = 1 liter 1 pound = grams

CONVERSION FACTORS What do conversion factors do? They let you change the units you are working with. How are we able to do this? We essentially multiply by 1.

SIGNIFICANT FIGURES Your calculator will lie to you. Not all the numbers on your calculator count in your answer. Significant Figures (sig figs) – are all the digits know with certainty plus one estimated digit.

RULE NUMBER 1 *All numbers that are not zero are significant. When you see any number that is not the number zero, it is significant. ALWAYS. Be sure and count them. *Example: 1812 has 4 significant figures.

RULE NUMBER 2 *Captive Zeroes always count as significant figures. When you see a zero and it is between two significant numbers then that zero is also significant. *Example: has 4 significant figures.

RULE NUMBER 3 *Trailing zeros are significant only if the number contains a decimal point. Trailing zeros are the zeros at the end of the number. If the number contains a decimal point then the trailing zeros are significant. If the number does not contain a decimal point then do not count the trailing zeros. *Example: has 4 significant figures.

RULE NUMBER 4 *Leading zeros do not count as significant figures. Leading zeros are at the front of the number. They are sometimes placeholders in decimal numbers. They do not count in the total of significant figures. *Example: has 3 significant figures.

ADDITION AND SUBTRACTION RULE *The number of decimal places in the result is equal to the number of decimal places in the least precise measurement. Less precise numbers have fewer decimal places. When added and subtracting, your answer should have the same number of decimal places as the number with least decimal places. *Example: = = 18.7

MULTIPLICATION AND DIVISION RULE *The number of sig figs in the result equals the number in the least precise measurement used in the calculation. Count the number of sig figs in each number in the calculation. Your answer will have the same number of sig figs as the lowest amount of sig figs in the calculation. *Example: 6.38 x 2.0 = = 13

EXACT NUMBERS *Exact numbers have an infinite number of sig figs. Exact numbers have either been measured precisely or have been counted. When determining the number of sig figs in your answer, do not use the exact numbers. *Examples: 1 inch = 2.54 cm1cal = J 1mL = 1cm 3

SCIENTIFIC NOTATION *It is a short way to write really big or really small numbers using the form M x 10 n. M represents the significant figures in the number and is written as a decimal between one and 10. n is the exponent and is the number of spaces the decimal point was moved.

SCIENTIFIC NOTATION 1) Insert an understood decimal point. *1) Insert an understood decimal point. *2) Decide where the decimal point will end up. *3) Count how many place you moved the decimal point *4) Re-write the number in short form. *5) Numbers greater than 1 have a positive exponent. *6) Numbers between 0 and 1 have a negative exponent

PRACTICE

SCIENTIFIC NOTATION *Use parentheses ( ) when calculating with numbers written in scientific notation. 4.3 x 10 5 / 2.1 x 10 3 = (4.3 x 10 5 ) / (2.1 x 10 3 ) =

EXACT NUMBERS & FORMULAS TO KNOW All METRIC TO METRIC conversion factors are EXACT All METRIC TO METRIC conversion factors are EXACT 2.54 cm = 1 inch 2.54 cm = 1 inch Time conversion factors are exact Time conversion factors are exact Density = mass / volume Volume = length * width * height

PROBLEM 1 The dosage of a certain antibiotic is 32 mg/kg of body weight. How much (grams) of the antibiotic must be given to an adult who weighs 85 kg? The dosage of a certain antibiotic is 32 mg/kg of body weight. How much (grams) of the antibiotic must be given to an adult who weighs 85 kg?

PROBLEM 2 The dosage of a certain anti-viral is 14.6 mg/kg of body weight per day. How much (grams) of the anti-viral must be given to an adult who weighs 145 lbs. during one week? The dosage of a certain anti-viral is 14.6 mg/kg of body weight per day. How much (grams) of the anti-viral must be given to an adult who weighs 145 lbs. during one week?

PROBLEM 3 The recommended dosage of a painkiller is 3.00 mg/kg of body weight per day. If a patient receives 245 mg of the painkiller, how much does the patient weigh (lbs.)? The recommended dosage of a painkiller is 3.00 mg/kg of body weight per day. If a patient receives 245 mg of the painkiller, how much does the patient weigh (lbs.)?

PROBLEM 4 The concentration of CO (carbon monoxide) is measured as 5.7 x µg / cm 3 inside a room. How many grams of CO are present in the room if the room’s dimensions are 3.5 m by 3.0 m by 3.2 m? The concentration of CO (carbon monoxide) is measured as 5.7 x µg / cm 3 inside a room. How many grams of CO are present in the room if the room’s dimensions are 3.5 m by 3.0 m by 3.2 m?

PROBLEM 5 A refinery produces a copper ingot weighing 150 lbs. If the copper is drawn into a wire whose diameter is 8.25 mm, how many feet of wire can be obtained? A refinery produces a copper ingot weighing 150 lbs. If the copper is drawn into a wire whose diameter is 8.25 mm, how many feet of wire can be obtained? The density of copper is 8.94 g / cm 3. The density of copper is 8.94 g / cm 3.

PROBLEM 6 If the concentration of Hg in a lake is determined to be 0.39 µg / mL, determine the total mass, in kg, of Hg in the lake. The lake has a surface area of 125 mi 2 and an average depth of 35 ft ft = 1 mi If the concentration of Hg in a lake is determined to be 0.39 µg / mL, determine the total mass, in kg, of Hg in the lake. The lake has a surface area of 125 mi 2 and an average depth of 35 ft ft = 1 mi