Metric Conversions and Scientific Notation

10 3 x x x x x x x x

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

How to convert w/in metric ex: convert 1 g to _____ kg 1. Go to Table C (turn it on its side & fill in blanks): 10 3 x x x x x x x x Kilo x x base deci centi milli x x micro x x nano x x pico k L,g,m d c m µ n p k L,g,m d c m µ n p 2. Place given value under appropriate prefix: 1g 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

Ex: Convert 97 pm to meters Ex: Convert 97 pm to meters to go from pico to base, move 12 to the left to go from pico to base, move 12 to the left ans: m ans: m Do you recall scientific notation? Do you recall scientific notation? ans: 9.7 x m ans: 9.7 x 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: 1 mm ans:.001 m ans:.001 m Ex cg = __________mg Ex 4. How many jumps and in what directions would you move the decimal to go from a pico measurement to a centi meaurement? 4280 Ans. 10 to the left (from 12 to 2)

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

7 CAN YOU RECOGNIZE SCIENTIFIC NOTATION? Is 23.5 x 10 6 in proper scientific notation? Is 23.5 x 10 6 in proper scientific notation? Is 0.48 x in proper scientific notation? Is 0.48 x in proper scientific notation? Is 6.04 x 10 1 in proper scientific notation? Is 6.04 x 10 1 in proper scientific notation? 2.35 x 10^7 4.8 x 10^-3

8 WHAT DOES THE EXPONENT IN SN DO? 1 x 10 2 = 10 2 = x 10 2 = 10 2 = x 10 1 = 10 1 = 10 1 x 10 1 = 10 1 = 10 1 x 10 0 = 10 0 = 1 1 x 10 0 = 10 0 = 1 1 x = = x = = x = = x = = 0.01 tells us the factor of 10 that the ‘M’ gets multiplied by

9 STANDARD -> SCIENTIFIC NOTATION Example: is in standard notation. Write it scientific notation Example: is in standard notation. Write it scientific notation place decimal after first non-zero number (fake location). 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 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 write number with decimal in fake location and with all the original sig figs x 10 n x x 10 -3

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

11 Try These: 13,000 = 13,000 = = = x = x = 4.90 x 10 4 = 4.90 x 10 4 = x 10 2 = x 10 2 = 1.3 x x x x x x10 3

from Quarks to Quasars ‘Power of 10’