(NR) Sept 23: Scientific Notation & Significant Digits

TO REMEMBER!
* Accuracy and precision is VERY important in science.
* Calculators are NOT smart enough to decide what is precise and what isn't.
* Scientists have established rules for rounding off extra digits; you MUST follow them!


SIGNIFICANT DIGITS

• Non-zero digits are always significant.
• If the zero is a place keeper it is not significant.
  example: 0.0098 (2 s.d.)
                0.00043 (2 s.d)
• Any numbers to the left of a decimal point are significant.
  example: 2.00, 27.06, 38.9000
• Zeros after another number are significant.

examples:

HOW MANY SIGNIFICANT DIGITS ARE IN...

14.78? ............_____s.d.
2.04? .............._____s.d.
9.00? .............._____s.d.
0.0038?..........._____s.d.

(answers: 4 s.d., 3 s.d., 3 s.d., 2 s.d.)

• when you multiply/divide ROUND to the number wit hthe fewest S.D.'s 
  example:
  
  
  • 1.38797 x 38.234 = 53.067644 => 53.068

• when adding/subtracting ROUND to the LEAST precise number
  example:
  
  
  • 10.978 - 5.68 = 5.298 => 5.30
  • 20.3 + 18.348 = 38.648 => 38.6
  
  http://www.youtube.com/watch?v=qrpq4qU6Wgg&feature=related 

SCIENTIFIC NOTATION

• used if we need to write the number 2000 with only 2 s.d.'s
  > 2.0 x 10 ^ 3
• used if we want to write the number thirty three billion four hundred million without taking up an entire line.
• Shows really big or really small numbers easily
• makes use of power of 10 

examples:
10^5 = 100000
10^-5 = 0.00001

-convert each question into scientific notation.

13400000 => ____ x 10^__
0.00000542 => ____ x 10^__
23900000 => ____ x 10^__

(answers: 1.34 x 10^7, 5.42 x 10^-6, 2.39 x 10^7)

REMEMBER:
DO NOT USE "^" ON YOUR CALCULATOR!!!