Metric Conversions and Scientific Notation

1. Metric Conversions and Scientific Notation

2. 102 101 100 10-4 10-5 10-7 10-8 10-10 1011 103 x x 100 10-1 10-2 10-3 x x 10-6 x x 10-9 x x 10-12

3. deci to micro -1 to -6 = 5 jumps to right for the decimal

4. How to convert w/in metricex: convert 1 g to _____ kg 1. Go to Table C (turn it on its side & fill in blanks): 103 x x 10010-1 10-210-3x x10-6x x 10-9 x x 10-12 Kilo x xbase decicentimillix x micro x xnanox xpico k L,g,m d c m µ n p 2. Place given value under appropriate prefix: 1g 3. Count how many jumps and in what direction decimal needs to move to get to desired unit 4. Move decimal and change unit symbol; fill jumps with zeros: .001 kg OR…subtract exponents, ex: 0 to 3 means 3 jumps

5. Ex: Convert 97 pm to meters to go from pico to base, move 12 to the left ans: .000000000097 m Do you recall scientific notation? ans: 9.7 x 10-11 m Ex 2: The head of a pin is about 1,000,000 nanometers in diameter. What is this measurement in mm? in m? ans: 1 mm ans: .001 m Ex 3. 482 cg = __________mg Ex 4. How many jumps and in what directions would you move the decimal to go from a pico measurement to a centimeaurement? 4280 Ans. 10 to the left (from 12 to 2)

6. SCIENTIFIC NOTATION • Used to write very LARGE and very smallnumbers w/o their zeros • always in the form of M x 10n • 1 ≤ M < 10 • therefore, decimal is always after 1st non-zero number • n = power of 10; represents decimal point jumps to convert from scientific to standard • ex: 6.45 x 10-5 m

7. CAN YOU RECOGNIZE SCIENTIFIC NOTATION? • Is 23.5 x 106 in proper scientific notation? • Is 0.48 x 10-2 in proper scientific notation? • Is 6.04 x 101 in proper scientific notation? 2.35 x 10^7 4.8 x 10^-3

8. WHAT DOES THE EXPONENT IN SN DO? • 1 x 102 = 102 = 100 • 1 x 101 = 101 = 10 • 1 x 100 = 100 = 1 • 1 x 10-1 = 10-1 = 0.1 • 1 x 10-2 = 10-2 = 0.01 tells us the factor of 10 that the ‘M’ gets multiplied by

9. STANDARD -> SCIENTIFIC NOTATION • Example: .004520 is in standard notation. Write it scientific notation • place decimal after first non-zero number (fake location). • count how many jumps you would have to take from the new fake location to get to the original location • in this case 3 jumps to the left so n = -3 • write number with decimal in fake location and with all the original sig figs x 10 n • 4.520 x 10-3

10. SCIENTIFIC NOTATION -> STANDARD • Example: 2.3 x 102 is in SN. Write it in non-SN (standard notation) • n=+2 therefore move decimal 2 places to the right • Fill in with zeros • 230

11. Try These: • 1.3 x104 • 1.08 x 10-3 • 0.3200 • 49 000 • 6.740x103 • 13,000 = • 0.00108 = • 3.200 x 10-1= • 4.90 x 104 = • 67.40 x 102 =

12. from Quarks to Quasars ‘Power of 10’