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## Converting Units

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**Converting Units**• Often, a measurement is more convenient in one unit but is needed in another unit for calculations. • Dimensional Analysis is a method for converting unit You may have learned another method of converting units in math or previous science classes…trust me…learn this one now! It will help you solve many other chemistry problems later in the class!**1 foot**12 inches Equivalents • Dimensional Analysis uses equivalents…what are they? 1 foot = 12 inches • What happens if you put one on top of the other?**1 foot**12 inches Equivalents • Dimensional Analysis uses equivalents…what are they? 1 foot = 12 inches • What happens if you put one on top of the other? When you put two things that are equal on top & on bottom, they cancel out and equal 1 = 1**Dimensional Analysis**• Dimensional analysis is based on the idea that you can multiply anything by 1 as many times as you want and you won’t change the physical meaning of the measurement! 1 27 inches = 27 inches**1 foot**12 inches Dimensional Analysis • Dimensional analysis is based on the idea that you can multiply anything by 1 as many times as you want and you won’t change the physical meaning of the measurement! 1 27 inches = 27 inches 27 inches = 2.25 feet**1 foot**12 inches Dimensional Analysis • Dimensional analysis is based on the idea that you can multiply anything by 1 as many times as you want and you won’t change the physical meaning of the measurement! Same physical meaning…it’s the same length either way! 1 27 inches = 27 inches 27 inches = 2.25 feet Remember…this equals “1”****27 inches 12 inches 1 foot 12 inches 1 foot 12 inches Canceling • Anything that is on the top and the bottom of an expression will cancel • When canceling units…just cancel the units… Unless the numbers cancel as well!**Steps for using Dimensional Analysis**1 Write down your given information Write down an answer blank and the desired unit on the right side of the problem space 2 Use equivalents to cancel unwanted unit and get desired unit. 3 Calculate the answer…multiply across the top & divide across the bottom of the expression 4**Common Equivalents**= 12 in 1 ft = 2.54 cm 1 in = 60 s 1 min = 3600 s 1 hr = 0.946 L 1 quart (qt) = 1 quart 4 pints = 454 g 1 pound (lb)**Example #1**1 Write down your given information Example: How many grams are equal to 1.25 pounds? 1.25 lb**Example #1**Write down an answer blank and the desired unit on the right side of the problem space 2 Example: How many grams are equal to 1.25 pounds? = ________ g 1.25 lb**Example #1**Use equivalents to cancel unwanted unit and get desired unit. 3 Example: How many grams are equal to 1.25 pounds? 454 g = ________ g 1.25 lb 1 lb Put the unit on bottom that you want to cancel out! The equivalent with these 2 units is: 1 lb = 454 g A tip is to arrange the units first and then fill in numbers later!**Example #1**Calculate the answer…multiply across the top & divide across the bottom of the expression 4 Example: How many grams are equal to 1.25 pounds? 454 g 568 = ________ g 1.25 lb 1 lb Enter into the calculator: 1.25 454 1**Metric Prefixes**• Metric prefixes can be used to form equivalents as well • First, you must know the common metric prefixes used in chemistry = 1000 kilo- (k) These prefixes work with any base unit, such as grams (g), liters (L), meters (m), seconds (s), etc. = 0.1 deci- (d) = 0.01 centi- (c) = 0.001 milli- (m) = 0.000001 micro- (μ) = 0.000000001 nano (n)**Metric Equivalents**• Many students confuse where to put the number shown in the previous chart…it always goes with the base unit (the one without a prefix) kilo = 1000 Example: Write a correct equivalent between “kg” and “g” • There are two options: • 1 kg = 1000 g • 1000 kg = 1 g To help you write correct equivalents, read the number that equals the prefix as the prefix itself in a “sentence”**Metric Equivalents**• Many students confuse where to put the number shown in the previous chart…it always goes with the base unit (the one without a prefix) kilo = 1000 Example: Write a correct equivalent between “kg” and “g” • There are two options: • 1 kg = 1000 g • 1000 kg = 1 g “1 kg is kilo-gram”…correct “kilo- kg is 1 gram”…incorrect To help you write correct equivalents, read the number that equals the prefix as the prefix itself in a “sentence”**Try More Metric Equivalents**Example: Write a correct equivalent between “mL” and “L” milli = 0.001 • There are two options: • 1 L = 0.001 mL • 0.001 L = 1 mL Example: Write a correct equivalent between “cm” and “m” centi = 0.01 • There are two options: • 1 cm = 0.01 m • 0.01 cm = 1 m**Try More Metric Equivalents**Example: Write a correct equivalent between “mL” and “L” milli = 0.001 • There are two options: • 1 L = 0.001 mL • 0.001 L = 1 mL “1 L is milli-mL”…incorrect “milli-liter is 1 mL”…correct Example: Write a correct equivalent between “cm” and “m” centi = 0.01 • There are two options: • 1 cm = 0.01 m • 0.01 cm = 1 m “1 cm is centi-meter”…correct “centi-cm is 1 m”…incorrect**height**width length Metric Volume Units • To find the volume of a cube, measure each side and calculate: length width height • But most chemicals aren’t nice, neat cubes! • Therefore, they defined 1 milliliter as equal to 1 cm3 (the volume of a cube with 1 cm as each side measurement) = 1 mL 1 cm3**Example #2**Example: How many grams are equal to 127.0 mg? = ________ g 127.0 mg • You want to convert between mg & g • “1 mg is 1 milli-g” • 1 mg = 0.001 g**Example #2**Example: How many grams are equal to 127.0 mg? 0.001 g 0.1270 = ________ g 127.0 mg 1 mg • You want to convert between mg & g • “1 mg is 1 milli-g” • 1 mg = 0.001 g Enter into the calculator: 127.0 0.001 1 You may be able to do this in your head…but practice the technique on the more simple problems so that you’ll be a dimensional analysis pro for the more difficult problems (like stoichiometry)!**Multi-step problems**• There isn’t always an equivalent that goes directly from where you are to where you want to go! • Rather than trying to determine a new equivalent, it’s faster to use more than one step in dimensional analysis! • This way you have fewer equivalents to remember and you’ll make mistakes more often • With multi-step problems, it’s often best to plug in units first, then go back and do numbers.**Example #3**Example: How many kilograms are equal to 345 cg? = _______ kg 345 cg • There is no equivalent between cg & kg • With metric units, you can always get to the base unit from any prefix! • And you can always get to any prefix from the base unit! • You can go from “cg” to “g” • Then you can go from “g” to “kg”**Example #3**Example: How many kilograms are equal to 345 cg? g kg = _______ kg 345 cg cg g Go to the base unit Go from the base unit**Example #3**Example: How many kilograms are equal to 345 cg? 0.01 g 1 kg = _______ kg 345 cg 1 1000 cg g 1 cg = 0.01 g 1000 g = 1 kg Remember—the # goes with the base unit & the “1” with the prefix!**Example #3**Example: How many kilograms are equal to 345 cg? 0.01 g 1 kg 0.00345 = _______ kg 345 cg 1 1000 cg g Enter into the calculator: 345 0.01 1 1 1000 Whenever dividing by more than 1 number, hit the divide key before EACH number! It doesn’t matter what order you type this in…you could multiply, divide, multiply divide if you wanted to!**Let’s Practice #1**Example: 0.250 kg is equal to how many grams?**Let’s Practice #1**Example: 0.250 kg is equal to how many grams? 1000 g 250. = ______ g 0.250 kg 1 kg 1 kg = 1000 g Enter into the calculator: 0.250 1000 1**Let’s Practice #2**Example: How many mL is equal to 2.78 L?**Let’s Practice #2**Example: How many mL is equal to 2.78 L? 1 mL 2780 = ______ mL 2.78 L .001 L 1 mL = 0.001 L Enter into the calculator: 2.78 1 0.001**Let’s Practice #3**Example: 147 cm3 is equal to how many liters?**Let’s Practice #3**Example: 147 cm3 is equal to how many liters? Remember—cm3 is a volume unit, not a length like meters! 1 mL 0.001 L 0.147 = _______ L 147 cm3 1 1 cm3 mL There isn’t one direct equivalent 1 cm3 = 1 mL 1 mL = 0.001 L Enter into the calculator: 147 1 0.001 1 1**Let’s Practice #4**Example: How many milligrams are equal to 0.275 kg?**Let’s Practice #4**Example: How many milligrams are equal to 0.275 kg? 1000 g 1 mg 275,000 = _______ mg 0.275 kg 1 0.001 kg g There isn’t one direct equivalent 1 kg = 1000 g 1 mg = 0.001 g Enter into the calculator: 0.275 1000 1 1 0.001