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Powers of Ten Vs Scientific Notation

Powers of Ten Vs Scientific Notation. How to tell the difference. Powers of Ten. Why do we need to know this? It is important to understand how we can express numbers that are VERY large or VERY small.

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Powers of Ten Vs Scientific Notation

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  1. Powers of TenVsScientific Notation How to tell the difference.

  2. Powers of Ten • Why do we need to know this? • It is important to understand how we can express numbers that are VERY large or VERY small. • Some circuit boards – you know, those weird looking things on the backs of machines – have holes with diameters as small as 10ˉ² or 0.01 of an inch. That is really, really small.

  3. A Circuit Board

  4. Sometimes people actually paint on just the head of a pin. They used a single hair to do the painting. Now that is small. This personpainted on the hair itself! Do you have that kind of patience?

  5. That is why we need ways to write smaller and larger numbers without always having to use all those zeros. Below is a chart to show you the difference between positive and negative powers of ten.

  6. What is the relationship between the positive powers of ten and the amount of zeros?What about the negative powers of ten?

  7. How can you multiply by a positive power of ten?

  8. How about dividing by a positive power of ten?

  9. Let’s check out the negative powers of ten.We’ll start with multiplying.

  10. Now for dividing negative powers of ten.

  11. Can we make this easier to remember? • Sure…just copy this chart down in your notes. • Now you can use it to study.

  12. Let’s try some problems with powers of ten. • 3.18 x 10³ Answer: • 3,180 • 106.9 ÷ 10³ Answer: • .1069 • 6,387 ÷ 10 ˉ² Answer: • 638,700 • 5.689 x 10 ˉ³ Answer: • .005689

  13. Now let’s look at Scientific Notation! • Over the last 500 years, there have been many methods and devices used to calculate the speed of light. • A scientist named Jean Bernard Leon Foucault measured the different angles at which light hit mirrors. • Another scientist named Olaus Roemer observed the frequent eclipses of Jupiter’s moon, Io.

  14. Light travels about 670,600,000 miles per hour. Scientific notation is used to write large and small numbers more easily. • A number written in scientific notation is expressed as a number that is greater than or equal to 1, but less than 10, multiplied by a power of ten. • In other words…

  15. In other words…(copy this for notes) • Move the decimal point until there is only a digit in the ones place. • Count the places you moved. • If you moved left, it will be a positive power of ten. • If you moved right, it will be a negative power of 10.

  16. Now, let’s write these numbers using Scientific Notation. • 0.023841 • Step 1 - move the decimal so there is only a digit in the ones place. 2.3841 • Step 2 – How many spaces did you move it? • Answer: 2 • Step 3 – Which way? • Answer: Right • So what is the scientific notation? • Answer: 2.2341 x 10 ˉ²

  17. Here are some more for you to try! • 0.00940051 Answer: • 9.40051 x 10ˉ³ • 728 Answer: • 7.28 x 10² • 0.06753 Answer: • 6.753 x 10ˉ²

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