Scientific Measurement and Significant Figures - Derived Units Density Concentration Calcium and Glucose Blood Levels and Regulation

Taking Measurements Need for Standards Basis of comparison – allows for proper communication of information if all are using the same system Le Systeme International d’Unite’s (SI) - International System aka – The Metric System

SI Units Measurement Unit Abbreviation Length Meter m Mass Gram g Volume Liter L Temperature Kelvin (or Celcius) K or (oC) Number of Particles Mole mol

Unit Multipliers Prefix Symbol Value Kilo K 103 deci d 10-1 centi c Purpose: allow the measurement to use reasonable numbers – make the numbers smaller or larger with a prefix in front of the unit to represent the magnitude (size) of the measurement Ex. Measuring the mass of a whale Prefix Symbol Value Kilo K 103 deci d 10-1 centi c 10-2 milli m 10-3

Prefix Symbol Value kilo k 103 deci d 10-1 centi c 10-2 milli m 10-3 Base Unit = gram 1 Kilogram = ______ grams 1 gram = ______ decigrams 1 gram = ______ centigrams 1 gram = ______ milligrams 1 deciliter = ______ centiliters 1 deciliter = ______ milliliters 1 centiliter = ______milliliters 1 milliliter = ______ microliters

Dealing With Very Large or Very Small Numbers Scientific Notation Uses powers of 10 to represent the magnitude of the number but keeping the same unit BIG NUMBERS – positive exponents Small numbers – negative exponents 23000  2.3 X 104 0.0054  5.4 X 10-3 Proper Notation – One number to the left of the decimal

Entering Scientific Notation into Your Calculator Ex: 5.4 X1016 Step 1: Enter “5.4” Step 2: Hit “2nd” key Step 3: Hit “,” key (Second function is “EE”) An “E” will appear Enter the exponent “16” Entered value should read “5.4E16” DO NOT USE “^” or “10^” or “10E”

Significance of a Measurement A Measurement can only be as accurate as the tool used to make it A tool will allow for exact numbers plus one decimal place of estimation These are known as SIGNIFICANT FIGURES These determine the basis of your calculations – the more accurate your measurement, the more accurate your calculations.

Correct Measurement? 11.6 cm 11.6283476 cm 11.65 cm

Correct Measurement? 12 12.0 12.00

Rules for Determining the Number of Significant Figures in a Given Measurement 1) All non-zeros are significant Ex: 23 m --- 2 sig figs.

Rules for Determining the Number of Significant Figures in a Given Measurement 2) Zeros between non-zeros are significant Ex: 203 m --- 3 sig figs. SIGNIFICANCE SANDWICH Zeros between two significant figures are significant 4005 m 50006 m 700008 m

Rules for Determining the Number of Significant Figures in a Given Measurement 3) Zeros after a decimal AND after a non-zero are significant Ex: 203.0 m --- 4 sig figs. 203.00 m --- 203.000000000 m --- REASON: These zeros show SPECIFICITY of the measurement – they show the accuracy of the tool

Rules for Determining the Number of Significant Figures in a Given Measurement 4) Zeros that act as PLACE HOLDERS only are NOT significant. EX: 2030 m --- only 3 sig figs 0.00203 m --- only 3 sig figs Both numbers can be written in a different form without sacrificing accuracy  Scientific Notation

Rules for Determining the Number of Significant Figures in a Given Measurement 5) Counting numbers, those that do not use a measuring device, are considered infinitely significant. Ex: 24 dogs Can’t get more accurate Only is important when they are used in a calculation.

SIG FIG Practice Measurement # Significant Figures 10.01 m 10.0 m 10 m 0.008910 km 23.010 L 100 Seniors

SIG FIG Practice Measurement # Significant Figures 10.01 m 4 10.0 m 0.008910 km 23.010 L 100 seniors

SIG FIG Practice Measurement # Significant Figures 10.01 m 4 10.0 m 3 0.008910 km 23.010 L 100 seniors

SIG FIG Practice Measurement # Significant Figures 10.01 m 4 10.0 m 3 0.008910 km 23.010 L 100 seniors

SIG FIG Practice Measurement # Significant Figures 10.01 m 4 10.0 m 3 0.008910 km 23.010 L 100 seniors

SIG FIG Practice Measurement # Significant Figures 10.01 m 4 10.0 m 3 5 0.008910 km 23.010 L 100 seniors

SIG FIG Practice Measurement # Significant Figures 10.01 m 4 10.0 m 3 5 0.008910 km 23.010 L 100 seniors

SIG FIG Practice Measurement # Significant Figures 10.01 m 4 10.0 m 3 5 0.008910 km 23.010 L 100 seniors

SIG FIG Practice Measurement # Significant Figures 10.01 m 4 10.0 m 3 5 0.008910 km 23.010 L 100 seniors Infinite

Math and Significant Figures A calculation can only be as accurate as the least accurate part

Addition and Subtraction Rules for Sig Figs. RULE: The answer can only have as many decimal places as the number with the fewest decimal places. Ex. 1.34 m + 2.5678 m = 3.9078 m Since 1.34 only has 2 decimal places, you must round your answer to 2 decimal places ACTUAL ANSWER = 3.91 m

Multiplication and Division Rules for Sig Figs. RULE: The answer can only have as many significant figures as the number with the fewest significant figures. Ex: 8.97 m X 5.2 m = 46.644 m2 Since 5.2 m only has 2 significant figures, you must express your answer with the first two significant figures beginning from the left hand side. ACTUAL ANSWER = 47 m2

PRACTICE 23.0 m + 45.678 m = 56.20 g / 25.6 cm3 = 12 dogs X 25.6 kg = 25.0 m x 100.0 m = 2.589542 cm + 4 cm = 456 cm x 456 cm X 10.5 cm =

PRACTICE 23.0 m + 45.678 m = 56.20 g / 25.6 cm3 = 12 dogs X 25.6 kg = 25.0 m x 100.0 m = 2.589542 cm + 4 cm = 456 cm x 456 cm X 10.5 cm = 68.7 m

PRACTICE 23.0 m + 45.678 m = 56.20 g / 25.6 cm3 = 12 dogs X 25.6 kg = 25.0 m x 100.0 m = 2.589542 cm + 4 cm = 456 cm x 456 cm X 10.5 cm = 68.7 m 2.20 g/cm3

PRACTICE 23.0 m + 45.678 m = 56.20 g / 25.6 cm3 = 12 dogs X 25.6 kg = 25.0 m x 100.0 m = 2.589542 cm + 4 cm = 456 cm x 456 cm X 10.5 cm = 68.7 m 2.20 g/cm3 307 kg

PRACTICE 23.0 m + 45.678 m = 56.20 g / 25.6 cm3 = 12 dogs X 25.6 kg = 25.0 m x 100.0 m = 2.589542 cm + 4 cm = 456 cm x 456 cm X 10.5 cm = 68.7 m 2.20 g/cm3 307 kg 2.50 X 103 m2

PRACTICE 23.0 m + 45.678 m = 56.20 g / 25.6 cm3 = 12 dogs X 25.6 kg = 25.0 m x 100.0 m = 2.589542 cm + 4 cm = 456 cm x 456 cm X 10.5 cm = 68.7 m 2.20 g/cm3 307 kg 2.50 X 103 m2 7 cm

PRACTICE 23.0 m + 45.678 m = 56.20 g / 25.6 cm3 = 12 dogs X 25.6 kg = 25.0 m x 100.0 m = 2.589542 cm + 4 cm = 456 cm x 456 cm X 10.5 cm = 68.7 m 2.20 g/cm3 307 kg 2.50 X 103 m2 7 cm 2180000 cm3

PRACTICE 23.0 m + 45.678 m = 56.20 g / 25.6 cm3 = 12 dogs X 25.6 kg = 25.0 m x 100.0 m = 2.589542 cm + 4 cm = 456 cm x 456 cm X 10.5 cm = 68.7 m 2.20 g/cm3 307 kg 2.50 X 103 m2 7 cm 2180000 cm3

Derived Units Two separate measurements combined by multiplication or division to DERIVE (make) a new measurement. Density: Combination of Mass and Volume by division - the concentration of matter in a specific volume.

Other measures of Concentration Parts per Million Measure of air and water pollution Measure of solute concentration - milligrams/Liter of solution (mg/L) Blood Chemistry Levels of Dissolved Materials: Milligrams per deciliter: mg/dL or mg/100 mL Ex: Calcium Levels = 10 mg/dL Glucose Levels = 90 mg/dL

Calcium Regulation Rigorous homeostatic control of blood calcium level is critical because calcium ions (Ca2+) are essential to the normal functioning of all cells, especially nerve and muscle cells.

When blood Ca2+ falls below the set point (10 mg/100 mL), parathyroid hormone (PTH) is released from four small structures, the parathyroid glands, embedded on the surface of the thyroid.

PTH raises the level of blood Ca2+ by direct and indirect effects. DIRECT: In bone, PTH induces specialized cells called osteoclasts to decompose the mineralized matrix of bone and release Ca2+ into the blood.

INDIRECT: In the kidneys, it promotes the conversion of vitamin D to its active hormonal form. An inactive form of vitamin D is obtained from food or synthesized in the skin. The active form of vitamin D acts directly on the intestines, stimulating the uptake of Ca2+ from food.

A rise in blood Ca2+ above the set point promotes release of calcitonin from the thyroid gland. Calcitonin exerts effects on bone and kidneys opposite those of PTH and thus lowers blood Ca2+ levels.

Glucose Regulation The pancreas has both endocrine and exocrine (excreting) functions. Its exocrine function is the secretion of bicarbonate ions and digestive enzymes, to the small intestine via the pancreatic duct. Clusters of endocrine cells, the islets of Langerhans, are scattered throughout the exocrine tissues of the pancreas.

Each islet has a population of alpha cells, which produce the hormone glucagon, and a population of beta cells, which produce the hormone insulin. Both hormones are secreted directly into the circulatory system

Insulin and glucagon are antagonistic hormones that regulate the concentration of glucose in the blood. Metabolic balance depends on maintaining blood glucose concentrations near a set point of about 90 mg/100 mL in humans.

When blood glucose exceeds this level, insulin is released and lowers blood glucose. When blood glucose falls below this level, glucagon is released and its effects increase blood glucose concentration by breaking down glycogen in the liver and the muscles.

Insulin lowers blood glucose levels by stimulating all body cells (except brain cells) to take up glucose from the blood. Brain cells can take up glucose without insulin and, thus, have access to circulating fuel at all times.