Countries that haven t adopted the Metric system yet

Transcription

1 Measurements

2 Countries that haven t adopted the Metric system yet

3 Customary Metric (Base Unit) International System (SI) Equivalents Length Mass inch, foot, yard, mile ounce, pound, ton Meter (m) Meter (m) 1m = 3.281ft 2.54cm = 1in Gram (g) Kilogram (kg) 454g = 1 lb Volume cup, pint, quart, gallon Liter (L) Cubic meter (m 3 ) 3.78L = 1 gal 1mL = 1cm 3 Time Second Second (s) Second (s) Same Temperature Fahrenheit ( F) Celsius ( C) Kelvin (K) 1 C = 1.8 F Amount of Substance Mole (mol) Mole (mol) same

4 Units of Measurement Volume is the amount of space a substance occupies.

5 Units of Measurement The mass of an object is the quantity of material it contains. You may be more familiar with the term weigh than with mass. The weight of an object depends on its mass and the pull on it by gravity. Therefore, the weight of an object changes as the gravitational pull changes. On the moon an object weighs much less than on Earth because the gravitational pull on the moon is much less. However, the mass is the same because the amount of material in that object is constant.

6 Units of Measurement

7 Units of measurement

8 Temperature For Celsius ( C), remember: 30 is warm, 20 is nice, 10 is cold, 0 is ice 37 C = 98.6 F (body temperature) 30 C = 86 F 20 C = 68 F (room temperature) 10 C = 50 F 0 C = 32 F (water freezes)

9 A Comparison of Temperatures Fahrenheit ( F) Celsius ( C) Kelvin (K) Sun A hot oven A desert A high fever Room temperature Water freezes A northern winter Helium boils Absolute zero

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12 Scientific Notation Scientific Notation is an efficient way to write very large and very small numbers. Width of a human hair 0.000,008m 8 x 10-6 m Hair on a human scalp 100,000 hairs 1 x 10 5 hairs

13 Scientific Notation Changing LARGE numbers Step 1: move the decimal to the left to make a number between 1 and 10 Step 2: count how many places the decimal point moved Step 3: write the number without all the zeros and multiply by a power of 10. The exponent tells how many places the decimal point was moved.

14 Scientific Notation Changing small numbers Step 1: move the decimal to the right to make a number between 1 and 10 Step 2: count how many places the decimal point moved Step 3: use a negative power of 10 to show how many places the decimal point was moved

15 Scientific Notation Changing back to standard form Step 1: check the sign of the exponent to know if it is a large or a small number - positive exponent = large number -negative exponent = small number Step 2: move the decimal the number and direction indicated by the exponent positive = right negative = left Step 3:write the number in standard form

16 Scientific Notation with large numbers Distance from the Sun (km) Planet Standard Scientific Mercury 57,000, x 10 7 Venus 108,000, x 10 8 Earth 150,000, x 10 8 Mars 228,000, x 10 8 Jupiter 779,000, x 10 8 Saturn 1,430,000, x 10 9 Uranus 2,880,000, x 10 9 Neptune 4,500,000, x 10 9

17 Scientific Notation with small numbers Microscopic Organism Standard Length (m) Scientific Ameoba x 10-4 Skin Cell x 10-5 Red Blood Cell x 10-6 Flu virus x 10-7 Ribosome x 10-8 trna x 10-9

18 Conversion Factor Used to convert from one unit to another Any equality can be written as 2 conversion factors (as fractions) Any conversion factor is the equivalent of the number one!

19 Conversion Factors Write the equality and conversion factors for each of the following: 1. One gallon is 4 quarts 1 gal=4qt and 2. There are 7 days in a week 7 days=1 week and 3. One gram is 1000mg 1 g=1000 mg and

20 Conversion Factors Write the equality and conversion factors for each of the following: 1. A bee flies at an average speed of 3.5 meters per second 3.5m=1sec and 2. An automobile traveled 46.0km on 1.0 gallon of gasoline 46.0km=1.0gal and 3. There are 20 drops in 1 milliliter of water 20 drops=1 ml and

21 Problem Solving with Conversion Factors Step 1: Given/Need State the initial unit given in the problem and the final unit needed. Step 2: Plan Equalities and Conversion Factors Write out a sequence of units that starts with the initial unit and progresses to the final unit for the answer. Be sure you can supply the equality for each unit conversion. Remember that equalities are derived from the metric system, the US system, and statements within a problem. Step 3: Set up Problem Write the initial quantity and unit and set up conversion factors that connect the units. Be sure to arrange the units in each factor so the unit in the denominator cancels the preceding unit in the numerator. Check that the units cancel properly to give the final unit. Carry out the calculations, count the significant figures in each measured number, and give a final answer.

22 Problem Solving with Conversion Factors Convert 165 lb to kilograms Step 1: Given/Need Given: 165 lb - Need: kilograms Step 2: Plan Convert US to Metric 1 kg = lb, Set up Problem or 165 lb x = 74.8 kg Choose the conversion factor fraction that cancels out the given units and leaves you with your needed units

23 Real Problems A recipe calls for 300 milliliters of water. You add 0.25 liters. Have you put in too much, too little, or the right amount? Determine which of the following measurements is largest: 1800 centimeters 2.1 meters kilometers You are told that you need a jar with a volume of at least 150 cm 3. The label on the jar you find says 0.16 liters. Can you use it?

24 Real Problems Worked Out

25 Using a factor from a word problem During a volcanic eruption on Mauna Loa, Hawaii, the lava flowed at a rate of 33 meters per minute. At this rate, how far in kilometers can the lava travel in 45 minutes?

26 Using a factor from a word problem Volcanic eruption problem solved Step 1: Given and Needed Given: 45 minutes of travel Need: Distance (in kilometers) Step 2: Plan Convert minutes to meters using information in the problem Convert meters to kilometers Step 3: Set Up the Problem See next slide

27 Using a factor from a word problem During travel, distance and time happen at the same time so our equality is and our conversion factors are and We also have the conversion factor of and Choose the conversion factors that cancel out the given units and move toward the needed units

28 Example problem from the homework The femur, or thigh bone, is the longest bone in the body. In a 6 foot tall person, the femur is 19.5 inches long. What is the length of that femur in millimeters? Equality: Conversion factors: Equality: Conversion factors: Use the conversion factor that cancels out the given units and moves towards the needed units

29 An interview with Deborah M. Gordon, Biologist, Ant researcher Students of biology have to study chemistry as well. How is chemistry relevant to ant behavior? -Ants don t see very well; they operate mostly by chemical communication. If you work on ants, you have to think about chemistry because chemicals are critically important in the ant s world. For example, the ants I study in Arizona use long-lasting chemical cues to identify themselves and to mark their nest area. Ants also use many short-term chemical cues called pheromones, which they secrete in certain situations. The best known are alarm pheromones, which are what make ants run around in circles when they re disturbed. Some ants secrete a pheromone from the tip of the abdomen that marks where they walk and creates a trail that other ants can follow. Ants have 12or 14 different glands that secrete different substances. We really don t now what they re all for, or how many chemical combinations an ant can respond to. In addition to chemicals used in communication, some ants produce antibiotics or chemical defenses against predators. Other ants use chemicals to kill certain plants.

30 Density Relationship of mass to volume How tightly packed a substance is Reported in g/ml or g/cm 3 for solids and liquids and as g/l for gases Finding the density of a metal sample can help to determine its purity.

31 Density

32 Densities of Some Common Substances Solids (at 25 C) Density (g/cm 3 or g/ml) Liquids (at 25 C) Density (g/ml) Gases (at 0 C) Density (g/l) Cork 0.26 Gasoline 0.66 Hydrogen Ice 0.92 Ethyl alcohol Helium Sugar 1.59 Olive oil 0.92 Methane Salt (NaCl) 2.16 Water (at 4 C) Neon 0.90 Aluminum 2.70 Milk 1.04 Nitrogen 1.25 Diamond 3.52 Mercury 13.6 Air (dry) 1.29 Copper 8.92 Oxygen 1.43 Silver 10.5 Carbon dioxide 1.96 Lead 11.3 Gold 19.3

33 Determining Density A block of aluminum occupies a volume of 15.0 ml and has a mass of 40.5 g. What is its density? What is the density of carbon dioxide gas if g occupies a volume of 100 ml? A sample of seawater weighs 158 g and has a volume of 156 ml. What is the denisty?

34 Determining Density of an Irregular Solid Measure the mass on a scale. Measure the volume by placing the object in a container of water with volume markings, and seeing how much the water level rises. Find the density of 227 g of marbles. When they are added to 425 ml of water the volume of water increases to 528 ml.

35 Density as a Conversion Factor If the density of milk is 1.04 g/ml, how many grams of milk are in 0.50 qt of milk? Given: 0.50qt, Need: g Plan: q (US to Metric) -> L (Metric factor) -> ml (Density factor) g 0.50qt * 1L/1.057qt * 1000mL/1L * 1.04g/1 ml = 490 g