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Simple Conversion Problems

Conversion Factors. There are many different ways to express the same amount.100 pennies = 1 dollar12 eggs = 1 dozen1 meter = 100 centimetersConversion Factors show these equal numbers as a ratio. . Conversion Factors. 100 pennies or 1 dollar 1 dollar 100 pennies 12 eggs

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Simple Conversion Problems

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    1. Simple Conversion Problems Section 4.2

    2. Conversion Factors There are many different ways to express the same amount. 100 pennies = 1 dollar 12 eggs = 1 dozen 1 meter = 100 centimeters Conversion Factors show these equal numbers as a ratio.

    3. Conversion Factors 100 pennies or 1 dollar 1 dollar 100 pennies 12 eggs or 1 dozen 1 dozen 12 eggs 1 meter or 100 centimeters 100 centimeters 1 meter

    4. Conversion Factors Think back to math class: What is 4 * 1? What is 4 * 1 / 1 ? When a conversion factor is expressed as a ratio, it is just like multiplying or dividing by 1. You are not actually changing the amount, just expressing it different with different units.

    5. Conversion Factors For example, 100 pennies = 1 dollar. If I have 4.38 dollars, that is the same as having 438 pennies. You know this from great practice growing up, but how did you do that calculation? 4.38 dollars x 100 pennies = 438 pennies 1 1 dollar

    6. Conversion Factors Both 4.38 dollars and 438 pennies are the same amount of money, just expressed differently using different units. Multiplying or diving by a conversion factor is just like multiplying or dividing by 1. The amount may look different with different units, but it still is equal to the original amount.

    7. Example 2 If a farmer has 3 dozen eggs, how many individual eggs does he have? 3 dozen x 12 eggs = 36 eggs 1 1 dozen 3 dozen and 36 eggs are the same amount of eggs, just expressed differently with different units.

    8. Dimensional Analysis Dimensional Analysis is a way to analyze and solve problems using the units of the measurements. This is what we use with conversion factors. You use this all the time without knowing it!

    9. Dimensional Analysis Your school club sold 600 tickets to a chili dinner fundraiser. You volunteered to help make the chili. The recipe you have serves 10 people, and calls for 2 tsp of chili powder. How much chili powder do you need for 600 people?

    10. Step 1: Analyze What do we know? servings = 600 10 servings = 2 tsp chili powder means: 10 servings or 2 tsp chili powder 2 tsp chili powder 10 servings What do we not know? amount of chili powder = ? Tsp What is our plan? use conversion to solve for the amount of chili powder needed in tsps.

    11. Step 2: Calculate You have 600 servings to make, but your answer needs to be in tsp of chili powder. This means you want the servings unit to cancel out and go away. This means you want to pick the conversion factor with servings in the denominator, making servings cancel. 600 servings x 2 tsp powder = 120 tsp chili powder 1 10 servings

    12. Step 3: Evaluate The question asked for an amount of chili powder in tsp. You found you need 120 tsp of chili powder. You answered the question. Good Job!

    13. Lets try another one! A lab experiment requires that every student has 7.5 mg of sulfur. The teacher has 50 students. How many grams of sulfur does the teacher need?

    14. Step 1: Analyze 1. What you know: 50 = students 7.5 mg = 1 student 2. What you dont know: 1 gram = ? Milligrams or 1 mg = ? G ? grams of sulfur What is my plan? I have two unknowns. However, I can figure out the first unknown using metric conversions. After that, I can find how many grams of sulfur the teacher needs.

    15. Step 2: Calculate I can look up that 1 gram = 1000 mg, so 1000 mg or 1 gram 1 gram 1000 mg Which one of these do I want? I want my answer to be in grams, so I want mg to cancel out. Lets remember this.

    16. Step 2: Calculate 50 students x 7.5 mg sulfur = 375 mg sulfur 1 1 student Step 3: Evaluate The question asked for grams of sulfur, and right now we have mg of sulfur. We are not done yet. We need to convert mg to grams. Back to step 2!

    17. Step 2: Calculate We have two conversion factors: 1000 mg or 1 gram 1 gram 1000 mg I have 375 mg. I want mg to cancel out, so I want them to be in the denominator. I choose the second conversion factor. 375 mg sulfur x 1 gram = 0.375 g sulfur 1 1000 mg The teacher needs 0.375 g of sulfur.

    18. Step 3: Evaluate The problem asked for how many grams of sulfur the teacher needed for her students. We found the amount of sulfur needed in grams. We are done! Yeah!

    19. Behold, the future.. Our next step is going to be combining these steps into one calculation, and maybe even adding on additional steps! 50 students x 7.5 mg sulfur x 1 gram = 0.375 g sulfur 1 1 student 1000 mg

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