Metric Metric Conversions Conversions

and and Scientific Scientific NotationNotation

101033 x x 10 x x 1000 10 10-1-1 10 10-2-2 10 10-3-3 x x 10 x x 10-6-6 x x 10 x x 10-9-9 x x x x 1010-12-12

101022 10 1011 101000

1010-10-10 10101111

1010-4-4 10 10-5-5

1010-7-7 10 10-8-8

deci to micro deci to micro

-1 to -6-1 to -6

= 5 jumps to right for the decimal= 5 jumps to right for the decimal

How to convert w/in metricHow to convert w/in metricex: convert 1 g to _____ kgex: convert 1 g to _____ kg

1. Go to Table C (turn it on its side & fill in blanks):1. Go to Table C (turn it on its side & fill in blanks):

101033 x x 10 x x 1000 10 10-1-1 10 10-2-2 10 10-3-3 x x 10 x x 10-6-6 x x 10 x x 10-9-9 x x 10 x x 10-12-12

Kilo Kilo x x x x base deci centi milli base deci centi milli x xx x micro micro x x x x nano nano x xx x pico pico

k L,g,m d c m µ n pk L,g,m d c m µ n p

2. Place given value under appropriate prefix:2. Place given value under appropriate prefix: 1g1g

3. Count how many jumps and in what direction 3. Count how many jumps and in what direction decimal needs to move to get to desired unitdecimal needs to move to get to desired unit

4. Move decimal and change unit symbol; fill 4. Move decimal and change unit symbol; fill jumps with zeros: .001 kgjumps with zeros: .001 kg

OR…subtract exponents, ex: 0 to 3 means 3 jumpsOR…subtract exponents, ex: 0 to 3 means 3 jumps

Ex: Convert 97 pm to metersEx: Convert 97 pm to meters

to go from pico to base, move 12 to the leftto go from pico to base, move 12 to the left

ans: .000000000097 mans: .000000000097 m

Do you recall scientific notation?Do you recall scientific notation?

ans: 9.7 x 10ans: 9.7 x 10-11-11 m m

Ex 2: The head of a pin is about 1,000,000 nanometers Ex 2: The head of a pin is about 1,000,000 nanometers in diameter. What is this measurement in mm? in in diameter. What is this measurement in mm? in m?m?

ans: 1 mmans: 1 mm

ans: .001 mans: .001 m

Ex 3. 482 cg = __________mgEx 3. 482 cg = __________mg

Ex 4. How many jumps and in what directions would you Ex 4. How many jumps and in what directions would you move the decimal to go from a pico measurement to move the decimal to go from a pico measurement to a centi meaurement?a centi meaurement?

4280

Ans. 10 to the left (from 12 to 2)

66

SCIENTIFIC NOTATIONSCIENTIFIC NOTATIONUsed to write very LARGE and Used to write very LARGE and

very very smallsmall numbers w/o their zeros numbers w/o their zeros always in the form of M x 10always in the form of M x 10nn

1 ≤ M < 101 ≤ M < 10– therefore, decimal is therefore, decimal is alwaysalways after after

11stst non-zero number non-zero numbern = power of 10; represents n = power of 10; represents

decimal point jumps to convert decimal point jumps to convert from scientific to standardfrom scientific to standard– ex: 6.45 x 10ex: 6.45 x 10-5-5 m m

77

CAN YOU RECOGNIZE CAN YOU RECOGNIZE SCIENTIFIC NOTATION?SCIENTIFIC NOTATION?

Is 23.5 x 10Is 23.5 x 1066 in proper in proper scientific notation?scientific notation?

Is 0.48 x 10Is 0.48 x 10-2-2 in proper in proper scientific notation?scientific notation?

Is 6.04 x 10Is 6.04 x 1011 in proper in proper scientific notation?scientific notation?

2.35 x 10^7

4.8 x 10^-3

88

WHAT DOES THE EXPONENT IN WHAT DOES THE EXPONENT IN SN DO?SN DO?

1 x 101 x 1022 = 10 = 1022 = 100 = 100 1 x 101 x 1011 = 10 = 1011 = 10 = 101 x 101 x 1000 = 10 = 100 0 = 1= 11 x 101 x 10-1-1 = 10 = 10-1-1 = 0.1 = 0.11 x 101 x 10-2-2 = 10 = 10-2-2 = 0.01 = 0.01

tells us the factor of 10 that tells us the factor of 10 that the ‘M’ gets multiplied bythe ‘M’ gets multiplied by

99

STANDARD -> SCIENTIFIC STANDARD -> SCIENTIFIC NOTATIONNOTATION

Example: .004520 is in standard notation. Example: .004520 is in standard notation. Write it scientific notationWrite it scientific notation

place decimal after first non-zero number place decimal after first non-zero number (fake location). (fake location).

count how many jumps you would have to count how many jumps you would have to take from the new fake location to get to take from the new fake location to get to the original locationthe original location– in this case 3 jumps to the left so n = -3in this case 3 jumps to the left so n = -3

write number with decimal in fake location write number with decimal in fake location and with all the original sig figs x 10 and with all the original sig figs x 10 nn

4.520 x 104.520 x 10-3-3

1010

SCIENTIFIC NOTATION -> SCIENTIFIC NOTATION -> STANDARDSTANDARD

Example: 2.3 x 10Example: 2.3 x 102 2 is in SN. is in SN. Write it in non-SN (standard Write it in non-SN (standard notation)notation)

n=+2 therefore move n=+2 therefore move decimal 2 places to the decimal 2 places to the rightright

Fill in with zerosFill in with zeros230230

1111

Try These:Try These:

13,000 =13,000 =0.00108 =0.00108 =3.200 x 103.200 x 10-1-1 = =4.90 x 104.90 x 1044 = =67.40 x 1067.40 x 1022 = =

1.3 x101.3 x1044

1.08 x 101.08 x 10-3-3

0.3200 0.3200 49 00049 0006.740x106.740x1033

from Quarks to Quasars ‘Power of 10’from Quarks to Quasars ‘Power of 10’