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← Percents - Visualizing Algebra

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Showing Revision 3 created 05/25/2016 by Udacity Robot.

  1. We're done working with exponents for now, but we'll come back to them later.
  2. Let's look at some other ways that we can use decimals. We're going to look at
  3. decimals and percents. Decimals and percents are often used in currency and in
  4. commercial business. We can buy shoes, sweaters, or electronics on sale. And we
  5. often want to know how much does something actually cost. By the end of this
  6. segment, you'll be able to find out how much an item cost, like a new pair of
  7. shoes. So, here's the problem that we're going to have you answer and come back
  8. to later. A pair of shoes costs $80 and is on sale for 44% off, what will you
  9. pay for the shoes? The first thing we need to recognize is this problem has a
  10. percent in it. Percent literally means per 100 or out of a 100. I can write
  11. 44 percent another way.
  12. I know it's 44 out of 100 or 44 divided by 100. 44 divided by 100 is the same
  13. thing as 0.44. Here's a grid of a 100 squares, or I have 1 block. Of these 100
  14. pieces, I'm going to have 44 of them. So, I'd have 10, 20, 30, 40, 44 blocks out
  15. of a 100 or 0.44 and that's this written as a decimal, 0.44. Okay, here are some
  16. other percents. I can have 23%, 6%, or 200%.
  17. I'm going to convert these percents to decimals. Sometimes, we need to convert
  18. percents to decimals in order to use them in problems or to multiply. Okay, so
  19. let's use these 100 blocks to help us out. Here, I have 23 squares shaded out of
  20. 100. So, 23 divided by 100. As a decimal, that's 0.23. For 6%, I'm going to have
  21. 6 blocks out of a 100. So, I have 6 blocks out of a 100 or 6 hundredths, 0.06
  22. Notice that 6 has to be in the hundredths spot. For 200%, I know that I have to
  23. do something different. I can color in 100 of the squares in this 1 block. So, I
  24. have a 100 blocks shaded, but I need 200%. This is only a hundred out of a
  25. hundred, that's a 100%. 200 percent means 200 out of 100. I know one of these
  26. squares represents a hundredth, so I have 200 hundred hundredths, or I just have
  27. 2 or 2 blocks. Okay. There's actually a pattern here that we want to notice.
  28. Let's look closely at the decimal places. Here in 23%, the decimal is here and
  29. then it ended up here. For 6%, the decimal started here and ended up here. For
  30. 200%, the decimal started here and ended up there.
  31. Let's have a quiz behind what's going on with this pattern. What do you notice?