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Normal form of Numbers

Normal form of Numbers. Water.. Can the water be also connected with normal form of numbers?. Lesson in Math,. Where you’ll learn, what is normal form of numbers. Which has a lot of valuable things for physics. In which you’ll learn how to write any number in normalform.

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Normal form of Numbers

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  1. Normal form of Numbers Water.. Can the water be also connected with normal form of numbers?

  2. Lesson in Math, • Where you’ll learn, what is normal form of numbers. • Which has a lot of valuable things for physics. • In which you’ll learn how to write any number in normalform. • And will learn how to do algebra with numbers in normal form...

  3. Normal form of numbers...

  4. Which of these numbers is in normal form? What does your intuitition tells you? • 5’000’000’000 • 0.0000000000099 • 343,9×10123 • 3,2×101234? «Press» the one number which might be the correct one 

  5. Not really correct... Click somewhere to continue...

  6. Absolutelly correct!  Click somewhere to continue...

  7. So the number in is a such number that has before its comma one significant number which is increased by order of 10: Normal Form Click on me! 

  8. Significant digits... • What are they? • As is known, number of digits is infinite, but digits are only 10. • Of them nine are significant... • Do you suspect, which ones? • Well then, of curse: • 1, 2, 3, 4, 5, 6, 7, 8, and 9 • 0 (zero) is NOT a significant number! • And now click on some spot on the screen!

  9. Writing number in normal form • Number in normal form can have a positive exponent to a multiplier 10: m – diameter of Jupiter, • Is used to express BIG numbers

  10. Writing number in normal form • Number in normal form also can have a negative exponent at the multiplier 10: m • Is used to express small numbers a nice picture (portrait) of water molecule

  11. Expressing numbers in normal form • 345’678=3,45678100’000=3,45678105 • Usually two numbers are left after comma:3,46105 • Sometimes comma is «carried»: • 345’678= + 5 10 345678 , , 5 If the number is without comma, then know, that it is «hiding» behind the last figure Now lets «carry» the comma, so that one significant figure is left before it! 5 Lets count, how many spaces has the comma «moved». The resulting number is the exponent of the 10 If the comma is «carried» to the left, then the power character is «+», and usually it is not written DONE! 

  12. Expressing the number in normal form • 0,0000012=1,20,000001=1,210-6 arasiz komata atstāj divus ciparus:6105 • In this situation also «carrying» comma is used: • 0,0000012 - 6 10 =1,2 , 6 4 3 2 5 1 , 6 Lets «carry» the comma, so that one significant number is left before it! 6 Count, how many places has the comma «carried» over BUT!!! The resulting number is exactly the exponent of 10 If the comma is «carried» to the right, then exponent character is «-»! DONE! 

  13. Working with numbers in normal form • Multiplication: • numbers are multiplied, exponents of 10 are summed • Check yourself: (remember the formula )= Press the space button when you’re finished calculating

  14. Working with numbers in normal form • Division: • numbers are divided and exponents of 10 are substracted • Check yourself: (remember the formula )= Press space button, when finished calculating Have you really calculated already ? 

  15. An example... • World ocean is 70,8% of Earth surface. It’s area is 361 million km². While surface of the land is 149 million km² • Despite its large surface area, World Ocean forms only 0,24% of Earth’s mass. • Knowing, that Earth has the mass of 5,971024 kg, calculate the total mass of World ocean! • Solution: • Calculate 0,24% of total mass:

  16. Working with numbers in normal form • Addition • Adding can be done with ony such numbers that have equal powers of ten, that is, numbers 10 have the same powers! Check yourself: Add numbers that are multiplied by powers of 10, while 10 with its power stays the same. Press space button when you’re done calculating

  17. In order to add.. In order for addition to be doable, sometimes normal form of the number has to be changed: or

  18. Examples of addition and substraction • = Press space when finished... When examples are done, its time for self-control tasks... Press space button! Press space when finished... Examples For self-control

  19. Just abit more.. for knowledge • Number in normal form can be raised, but then the formula has to be remembered • For example: • Root can also be gained from number normal form (the same formula will work) • For example:

  20. Almost at the finish • Advantages: • Very small and very big numbers can be written; • No need to count zeros; • The same units of measurment can be used to measure both big and small amounts (no need to know decimal prefixes). • Disadvantages: • Looks unusual; • Won’t be understood in shop; • Several formulas has to be known in order to calculate.

  21. Ideas for further independent work I – human... Water in me... Mass of one water molecule... What could be calculated, what information and where to find it? Planet Earth... Equator... Size of water molecule... Belt... What could be calculated, what information and where to find it?

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