Algebra 1 > Notes > Yorkcounty Final > Unit 5 > Lesson 11 - Scientific_notation

Scientific Notation

Lesson 11

What is Scientific Notation?  Scientific

Notation uses powers of 10 to express decimal number.  2.4 X 104 = 24000  2.4 X 10-4 = .00024  NOTE:

power.

2.4 X 104 reads 2.4 times 10 to the 4th

Scientific Notation  Numbers

in scientific notation are written a X 10n , where a is greater than or equal to 1 and less than to. 1 < a < 10

Reading Scientific Notation  

 

4.5 X 103 You take the decimal and move it right 3 places. The exponent is positive 3, that means move the decimal 3 places to the right. If the decimal was negative you would move the decimal to the left. After moving the decimal 3 places to the right we get 4500. When you move the decimal to the left or right and there is no number there, you fill that gap in with a zero.

Reading Scientific Notation 4

50 0.

 We

took 4.5 X 103 and moved the decimal place 3 to the right. I filled in every gap with a zero.

 Now

we have 4500

Literal Meaning  So

we know that 4.5 X 103 is 4500. Let me prove this to you in a way you understand.

 103,  4.5

(10 . 10 . 10),

is the same as 1000

X 103  4.5 X 1000 = 4500

Writing in scientific notation     



Write 35000 in scientific notation. Is 35000 between 1 and 10? NO! What we need to do is move the decimal place over so we can make it between 1 and 10. 3.5000 is between 1 and 10. We moved the decimal place left 4 places. Now here is the trick to writing it in scientific notation. We now have our “a” which is between 1 and 10. If we were to write 3.5000 as 35000 we would have to move the decimal 4 places to the RIGHT. So, 3.5 X 104 , is the same as 35000.

Try this one  Write  Is

5206 in scientific notation.

5206 between 1 and 10? NO!  5.206 is though. I moved the decimal 3 places to the left.  If I wanted to write 5.206 as 5206 I would move my decimal place 3 to the right.  5.206 X 103 = 5206

Going to the left  .000452

, write in scientific notation  .000452 is not between 1 and 10.  4.52 is between 1 and 10 (move 4 decimal places to the right)  To get 4.52 back to .000452 you would have to move the decimal 4 places to the left.  4.52 X 10-4 = .000452

Try these two  Write

in scientific notation

 82400  .0000224

Answers 

82400 = 8.24 X 104 – –



82400 is not between 1 and 10. 8.24 is between 1 and 10. We got there by moving the decimal 4 places to the left. To get it back to the original we need to move the decimal 4 places to the right.

.0000224 = 2.24 X 10-5 – –

.0000224 is not between 1 and 10. 2.24 is between 1 and 10. We got there by moving the decimal 5 places to the right. To get it back to the original we need to move the decimal 5 places to the left.

Word Problems 

4.4 X 107 diapers are thrown away each day. How many are thrown away each year? Show your answer in scientific notation.



There are 365 days per year. We want to take the rate of trashed diapers per day and multiply it to 365. (4.4 X 107) . (365) It would be easier to complete this problem if you put 365 in scientific notation. 365 = 3.65 X 102 (4.4 X 107)(3.65 X 102) , rewrite the problem so you are multiplying like terms. (4.4 . 3.65)(107 . 102) (NOTE: multiply same bases, add exponents!) (16.06)(109) , we must change 16.06 into scientific notation (1.606 X 101)(109) = (1.606 X 101 X 109) = 1.606 X 1010

     

Word Problem A

whale has a mass of 1.0 X 105 kilograms.  A school of 125 whales were spotted off the coast of Alaska. What is the total mass of the school? Express your answer in scientific notation.  Try

this on your own. Answer on next slide.

Answer  (1.0

X 105) . (125)  (1.0 X 105) . (1.25 X 102)  (1.0 . 1.25)(105 . 102)  (1.25)(107) = 1.25 X 107  1.25

X 107 = 12,500,000 kilograms- That is a heavy school of whales!