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## D imensional Analysis Conversions

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**Dimensional Analysis Conversions**With Significant Digits!**Other Metric Mentionables**• For ALL substances: 1 mL = 1cm3 • Water is special: • 1 gram of has a volume of 1 ml or 1 cm3 • 1 g water = 1mL water • 1 g water =1 cm3 water**Let’s Do It!!!**• Write the numbers 1-5 on your paper. • Write which of these values is larger: • 1. A microliter or a liter • 2. A kilogram or a gram • 3. A centiliter or a liter • 4. A megasecond or a second • 5. A decigram or a gram**Let’s Do It!!!**• Write the numbers 1-5 on your paper. • Write which of these values is larger: • 1. A microliter or a liter • 2. A kilogram or a gram • 3. A centiliter or a liter • 4. A megasecond or a second • 5. A decigram or a gram**Let’s Do It!!!**• Write the numbers 1-5 on your paper. • How many ____________ are in a ____________: • 1. micrograms in a gram • 2. meters in a kilometer • 3. centiliters in a liter • 4. seconds in a megasecond • 5. decigrams in a gram**Let’s Do It!!!**• Write the numbers 1-5 on your paper. • How many ____________ are in a ____________: • 1. micrograms in a gram 1,000,000 or 1X106 • 2. kilometers in a meter 1000 or 1X10-3 • 3. centiliters in a liter 100 or 1X102 • 4. megaseconds in a second 1,000,000 or 1X10-6 • 5. decigrams in a gram 10 or 1X101**Conversions**• How many kilometers are in 50 meters? • This can get a little hairy! • How many inches in a meter? • Now we are trying to relate English units and metric units! Even more confusing! • This is where we will use a technique called ……. (drum roll please) • DIMENSIONAL ANALYSIS!!!!!!!!**Dimensional Analysis What is it?**• A problem solving method • A series of multiplications and divisions • Units are also multiplied and divided (units can cancel) • We multiply by fractions called “conversion factors” • Conversion factor- a statement of fact expressed as a fraction equaling one that helps us convert from one unit to another**Conversion Factors**• All conversion factors are equal to 1 • Conversion factors can be made from • English-English relationships • 1 foot = 12 inches • Metric-Metric relationships • 1 km = 1x103m • English-Metric relationships • 1.00 in = 2.54 cm • Conversion factors can be made from information given in a problem**Equal to 1???**Conversion factors are made from equivalents 2 = 2 X = X 4 - 2 = 1 + 1 1 foot = 12 inches**Equivalent**1 foot = 12 inches 1 km = 1 x 103 m Conversion Factor 1 cm = 1 x 10-2 m**Metric Conversions**• Fact: 1 kilometer = 1000 meters from our table • This is a conversion factor and we can write it 2 ways: a. 1 km or b. 1000 m 1000 m 1 km What do these mean? The exact same thing! a. That there is 1 km PER 1000 m or 1 km = 1000m b. That there are 1000 m PER 1 km or 1000m = 1 km Both the top and bottom are equal so the whole conversion factor is equal to one so we can use it without randomly changing values**Metric Conversions**• So….. • How many kilometers ARE there in 50 meters? • We can use a conversion factor that relates km to meters, but which one? a. 1 km or b. 1000 m 1000 m 1 km**Question Mark Format-Reference**• We follow some steps and the UNITS WILL TELL US WHAT TO DO. • Follow this QUESTION MARK FORMAT, when doing dimensional analysis! Even if you can solve it in your head, these questions will get a LOT tougher! • FOLLOW THE METHOD!!!! • DID I SAY FOLLOW THE METHOD??????**Question Mark Format-Reference**• PSSSSTTTT. FOLLOW THE METHOD • 1. Start every problem with the QUESTION MARK FORMAT (the “?” means “how many?”) • 2. Cancel the units • 3. Insert fact • 4. Do the math (multiply across and divide top by bottom just like fractions) How many kilometers in 50 meters? • ? km = 50 m**Metric Conversions**• PSSSSTTTT. FOLLOW THE METHOD • 1. Start every problem with the QUESTION MARK FORMAT (the “?” means “how many?”) • 2. Cancel the units • 3. Insert fact • 4. Do the math (multiply across and divide top by bottom just like fractions) How many kilometers in 50 meters? • ? km = 50 m x ____km__ m**Metric Conversions**• PSSSSTTTT. FOLLOW THE METHOD • 1. Start every problem with the QUESTION MARK FORMAT (the “?” means “how many?”) • 2. Cancel the units • 3. Insert fact • 4. Do the math (multiply across and divide top by bottom just like fractions) How many kilometers in 50 meters? • ? km = 50 m x _____ km__ m**Metric Conversions**• PSSSSTTTT. FOLLOW THE METHOD • 1. Start every problem with the QUESTION MARK FORMAT (the “?” means “how many?”) • 2. Cancel the units • 3. Insert fact • 4. Do the math (multiply across and divide top by bottom just like fractions) How many kilometers in 50 meters? • ? km = 50 m x __1__km__ 1000 m**Metric Conversions**• PSSSSTTTT. FOLLOW THE METHOD • 1. Start every problem with the QUESTION MARK FORMAT (the “?” means “how many?”) • 2. Cancel the units • 3. Insert fact • 4. Do the math (multiply across and divide top by bottom just like fractions) How many kilometers in 50 meters? • ? km = 50 m x __1__km_ = 50 X 1 km = ? 1000 m 1000**Reference**1 ft = 12 in • Convert 7.0 feet to inches ? in =**Reference**1hg=1*102g • Convert 2.89 hg to g • ? g=**Reference**1Mg=1*106g 1cg=1*10-2g • Convert 2.89 Mg to cg • ? cg =**Let’s Do It!!!!**• 1. How many kilograms are in a 350 grams? • 2. I have 45 milliliters. How liters is this? • 3. Superchallenge!!! How many kilometers are in a millimeter? You have to use two conversion factors!**Metric ConversionsMetric video 8 min**• One last important step: • CHECK SIGNIFICANT DIGITS! • Any fact that is found in a conversion factor is not a measurement and so is ignored when calculating the number of significant digits.**Reference**1dm=1*10-1m 1.00m=39.4in 12in=1ft 3ft=1yd • Convert 4.756 dm to yd • ? yd= measureddefinition measured definitiondefinition 4 SD NO SD 3 SD NO SDNO SD**1 g water = 1 mL**How many pounds are in a gallon of water? • ? lb=**Dimensional Analysis with Multiple Units- Reference**Strategy: 1. Convert each unit in the fraction separately 2. Make sure units cancel!**Reference**1 mi = 5280 ft 1 ft = 12 in 39.4in = 1.00m 1x103m = 1km 1hr = 60 min 1 min = 60 sec Example 1: Convert 70.0 mi/hr to km/sec • ? km/sec =**454g = 1.00lb**.946L = 1.00qt 4qt = 1gal Example 2: • Convert 15.3 g/L to lb/gal • ? lb/gal =**Let’s Do It!!!!**• 1. How many Megagrams are in a pound? • 2. I have 45 liters. How many cm3 is this?**ReviewDimensional Analysis video 9min**• Number your paper from 1-5 and answer the following questions. • 1. Which of these has 3 significant digits? • a. 0.000000312 • b. 3.5 X 104 • c. 0.4506 • d. 910**Review**• A • 2. Which of these is a qualitative observation? • a. the sky is dark • b. his head is 45 cm in diameter • c. she has 20 freckles • d. the candle was 17 cm long**Review**• A • 3. Which of these is a conversion factor? • a. 3 cm • b. 12 inches = 1 foot • c. 3 ft 1 yard**Review**• C • 4. What’s the first step in setting up a dimensional analysis problem? • a. cancel the units • b. write down all the conversion factors • c. cry • d. set up the question mark format**Review**• D • 5. What does this conversion factor mean? 14 frizzles drizzle • a. There are drizzles that are frizzles • b. There are 14 frizzles per drizzle • c. A frizzle and a drizzle are equal • d. There are 14 drizzles per frizzle**Review**• B What observations can you make about this picture?**Density**• Density = mass per (divided by) unit volume • D = mass/volume • D= m/V • Common units of density: g/mL, g/cm3 • Remember that 1 mL=1cm3 ! • Suppose we have an object with a mass of 5.0 grams and a volume of 2.0 mL. What would be the density? • D = 5.0g/2.0mL = 2.5g/mL (2 sig figs)**Let’s Do It!!!**• 1. Given a mass of 12g and a volume of 3 mL, calculate the density.**Let’s Do It!!!**• 1. Given a mass of 12g and a volume of 3 mL, calculate the density. • Need density • D = m/V • D = 12g/3mL • D = 4m/mL (1 sig fig since following multiplication rules**Let’s Do It!!!**• 2. Given that the density of iron is 7.9m/cm3 what would be the volume of a 15.8 g piece of iron?**Let’s Do It!!!**• 2. Given that the density of iron is 7.9g/cm3 what would be the volume of a 15.8 g piece of iron? • D = m and asking for volume so solve for V V • Multiply both sides by V: V x D = m x V V So V x D = m • Divide both sides by D: V x D = m D D So V = m = 15.8g = 2.00 cm3(3 sig figs) D 7.9g/cm3**Let’s Do It!!!**• 3. Find the density of a block with a length of 4.0cm, width of 3.0cm, and a height of 2.0cm and a mass of 36g**Let’s Do It!!!**• 3. Find the density of a block with a length of 4.0cm, width of 3.0cm, and a height of 2.0cm and a mass of 36g • Need density • D = m/V • V = l x w x h = 4.0cm x 3.0cm x 2.0cm = 24cm3 • D = 36g/24cm3 or 1.5g/cm3**Review**• Number your paper from 1-5 and answer the questions that follow • 1. Which of these is correct? • A. 1 gram = 1 x 10-3 milligrams • B. 1 gram = 1 x 106 kilograms • C. 1 gram = 1 x 103 milligrams • D. 1 gram = 1 x 10-6 micrograms**Review**• C • Round to the appropriate significant digit • 2. If I dropped a toy car into a glass and the toy car displaced 20mL of water, what is the volume of the toy? • A. 20cm • B. 2mL • C. 20mm • D. 20cm3**Review**• D • 3. What is the mass of an object with a density of 4.0g/cm3 that displaces 3.0 cm3 of water? • A. 7 g • B. 12 g • C. 0.75 g • D. 1 g**Review**• B • 4. What is the mass of 50mL of water?**Review**• 1 g = 1 mL = 1 cm3 of water, so 50mL = 50g • D = m/V not needed! • 5. Super challenge! You have a piece of silver with a mass of 31.5 g. Silver has a density of 10.5g/cm3 . What would be the new level of water if this piece of silver is placed into 15mL of water? • A. 12.0mL • B. 5.0mL • C. 18.0mL • D. 21.0 mL**Review**• C • Solve D = m/V • So V = m = 31.5g = 3.00cm3 = 3.00mL D 10.5g/cm3 So add 15.0 mL + 3.00mL = 18.0mL