Part I: Discussing Percents/Decimals/Fractions and Conversions
Task Background: There are different ways of representing the same value of a number. For instance, 0.5 (a decimal) is equivalent to 50% (a percentage) and to 1/2 (a fraction). Conversions such as these are needed in many applicable areas, such as interest on a loan, calculating savings on discounts, measuring an amount of medicine administered to a patient, and buying a certain amount of carpet.
Primary Task Response: Within the Discussion Board area, write 3–4 paragraphs that respond to the following questions with your thoughts, ideas, and comments. This will be the foundation for future discussions by your classmates. Be substantive and clear, and use examples to reinforce your ideas:
Task Assignment: There are specific procedures to convert a value from decimal to percentage (and vice versa), from a fraction to a percentage (and vice versa), and from a decimal to a fraction (and vice versa). Select 2 of the following examples (1 of them being a problem from your major, if applicable) [I chose medical and business], and for each of them, complete the following:
Explain in words the procedure you followed for each of your calculations.
Be sure to show all your steps when applicable.
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Business
Many interest rates, such as those on car loans, credit cards, and home loans, are given in as a percent. However, if you need to make any calculations with the percent interest rate, you must convert it to a decimal.
Research and find the interest rate, as a percent, for a particular credit card.
Let’s pretend that Olaf is a student joing going to college for the first time. He has never had a credit card before, so he doesn’t have what is called a credit history. Nonetheless, Olaf after research discovers that he can get a special student Discover Card for the great rate of 12.99%
Change the interest rate percent to a decimal and then to a fraction.
Olaf wants to know the percent rate as a decimal number. His mother shows him how to change the interest rate to a decimal number. She tells him, “drop the % sign and multiply by .01” and he follows her advice.
“Now how does one change the interest rate to a fraction,” Olaf asks him mother. “Find the decimal number, then divide it by 100, but write the division as a fraction,” says his mother.
If you wanted to compare your researched rate to 12 1/5%, how could you change this percent to a decimal?
Olaf had heard that a new acquaintance of his at college had a truly phenomenal rate at his bank of . He wanted to compare the two differing rates, but was unsure if he knew the appropriate method. Another consultation with his mother, who had finished college, resulted in the following stratety: First, rewrite the fraction part as a decimal by dividing the numerator by the denominator (you might have to round off sometimes, but he didn’t need to this time).
so
then, his mother confirmed his own strategy,change the percent to a decimal by dropping the % sign and multiplying by .01
Compare the 12 1/5% to your researched interest rate, and explain which interest rate is better.
So now Olaf was able to compare the diverse rates. A quick perusal of the data showed him that . In other words the .122 rate was better than the .1299 rate; and his acquaintance was shown to truly have had the better rate at
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Medical
It is important that physicians know how long a medicine will stay in a person’s body to keep a sufficient amount so the person does not overdose. For example, a patient takes a pill that has a dosage of 50 mg. (milligrams) and wakes up the next day with a particular percentage of the medication washed out.
Demonstrate your knowledge of conversions by first choosing a percentage of the medicine that is washed out the next day, and then convert this percentage to a decimal] and then a fraction.
Mrs. Delatorres was taking a prescription medicine, of which her system would wash out 20% each day. [20% = 20 x .01 = .2] Mrs. Delatorres wanted to convert this percentage to a decimal number. She changed the .2 to a fraction by saying the decimal correctly (two tenths) and then writing down what she heard. Mrs. Delatorres then reduced the fraction to 1/5[.2 = 2/10 = 1/5].
How much medication remains in the body after the percentage amount of your choosing is washed out?
Mrs. Delatorres knew that when working with percentages “all” is almost always 100%. Given that 20% was washed out, she then subtracted 20% from 100% to find out how much percentage is left in the body and arrived at 100% - 20% = 80% left in the body.
Discussion:
I saw how much easier it is to compare rates when they are written the same way, whether it is as decimal numbers or fractional remainders. But since it is hard to compare different fractions, I concluded that decimal representations would be more practical – it would be easiest if all the rates were written as decimal percents. That means if the percentage has a fraction inside it, I have to write the fraction as a decimal like I did in the interest rate problem.
I also see how you can talk about what something does without exactly knowing what quantity it is. For example, in the medical problem, I never knew how much medicine the person was taking. But I used percents. Things were made easy because 100% meant all of the medicine, even if I didn’t know the real amount. And then I could use percents to talk about how much would be washed out and how much would be left behind. I never knew the real amounts, but I could still talk about it.
What’s nice about being able to talk about something using percents when you don’t know how much is really there is that you can still compare different things. Like, if 90% of a medicine was washed out of an adult, but only 30% was washed out of a child, then maybe a child shouldn’t take that medicine. That’s because 10% would be left in the adult, but 70% would be left in the child. It’s easier to think about things when you understand percents.