9/10/12 Metric Conversions Dimensional Analysis (Using Conversion Factors) 1 dollar=4 quarters=10 dimes=20 nickels=100 pennies 1 dollar=4 quarters=10 dimes=20 nickels=100 pennies How many nickels would a bank give you in exchange for 63 quarters? We can use statements of equality to solve problems by a method known as Dimensional Analysis How many nickels are equivalent to how many quarters? If you went to the bank with 63 quarters and asked to exchange them for nickels, how many nickels would you get in return? 1 quarter = 5 nickels If you look at the statement at the top, you will noMce that: 4 quarters = 20 nickels The use of dimensional Analysis (also called the Conversion Factor method) can answer the quesMon. Each area of blue text on this page is an example of a statement of equality 1 dollar=4 quarters=10 dimes=20 nickels=100 pennies 1 dollar=4 quarters=10 dimes=20 nickels=100 pennies If you went to the bank with 63 quarters and asked to exchange them for nickels, how many nickels would you get in return? If you went to the bank with 63 quarters and asked to exchange them for nickels, how many nickels would you get in return? To set up a conversion factor solu>on follow these steps: To set up a conversion factor solu>on follow these steps: 1. Write down the number and the unit of the known quanMty. In this example that would be: 2. Place a blank conversion factor next to it, followed by an equal sign: 63 quarters ! $
63 quarters # & =
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1 9/10/12 1 dollar=4 quarters=10 dimes=20 nickels=100 pennies 1 dollar=4 quarters=10 dimes=20 nickels=100 pennies If you went to the bank with 63 quarters and asked to exchange them for nickels, how many nickels would you get in return? If you went to the bank with 63 quarters and asked to exchange them for nickels, how many nickels would you get in return? To set up a conversion factor solu>on follow these steps: To set up a conversion factor solu>on follow these steps: 3. ATer the equal sign, leave space for the answer and then place the unit that the answer should have: 4. Carefully place units correctly inside the blank conversion factor: ! $
63 quarters # & =
" %
nickels
!
63 quarters #
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nickels $
&=
quarters %
nickels
1 dollar=4 quarters=10 dimes=20 nickels=100 pennies 1 dollar=4 quarters=10 dimes=20 nickels=100 pennies If you went to the bank with 63 quarters and asked to exchange them for nickels, how many nickels would you get in return? If you went to the bank with 63 quarters and asked to exchange them for nickels, how many nickels would you get in return? To set up a conversion factor solu>on follow these steps: To set up a conversion factor solu>on follow these steps: 5. Carefully place the correct numbers inside the blank conversion factor: Calculate the numerical answer: ! 20 nickels $
63 quarters #
&=
" 4 quarters %
nickels
! 20 nickels $
63 quarters #
& = 315 nickels
" 4 quarters %
109nm = 106μm = 103mm = 102cm = 101dm = 100meter 100meter = 10-­‐3 km = 10-­‐6 Mm = 10-­‐9Gm = 10-­‐12Tm 109nm = 106μm = 103mm = 102cm = 101dm = 100meter 100meter = 10-­‐3 km = 10-­‐6 Mm = 10-­‐9Gm = 10-­‐12Tm How many mg are equivalent to 3.2x10-­‐5kg? "
3.2x10 !5 kg $
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How many mg are equivalent to 3.2x10-­‐5kg? "
3.2x10 !5 kg $
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2 9/10/12 109nm = 106μm = 103mm = 102cm = 101dm = 100meter 100meter = 10-­‐3 km = 10-­‐6 Mm = 10-­‐9Gm = 10-­‐12Tm How many mg are equivalent to 3.2x10-­‐5kg? 109nm = 106μm = 103mm = 102cm = 101dm = 100meter 100meter = 10-­‐3 km = 10-­‐6 Mm = 10-­‐9Gm = 10-­‐12Tm How many mg are equivalent to 3.2x10-­‐5kg? " 10 3 mg %
3.2x10 !5 kg $ !3 ' = mg
# 10 kg &
" 10 3 mg %
3.2x10 !5 kg $ !3 ' = 32 mg
# 10 kg &
109nm = 106μm = 103mm = 102cm = 101dm = 100meter 100meter = 10-­‐3 km = 10-­‐6 Mm = 10-­‐9Gm = 10-­‐12Tm 109nm = 106μm = 103mm = 102cm = 101dm = 100meter 100meter = 10-­‐3 km = 10-­‐6 Mm = 10-­‐9Gm = 10-­‐12Tm How many μL are equivalent to 3.2x10-­‐4ML? How many μL are equivalent to 3.2x10-­‐4ML? " 10 6 µ L %
8
3.2x10 !4 ML $ !6
' = 3.2x10 µ L
# 10 ML &
" 10 6 µ L %
8
3.2x10 !4 ML $ !6
' = 3.2x10 µ L
# 10 ML &
109nm = 106μm = 103mm = 102cm = 101dm = 100meter 100meter = 10-­‐3 km = 10-­‐6 Mm = 10-­‐9Gm = 10-­‐12Tm How many ng are equivalent to 3.2x10-­‐14kg? " 10 9 ng %
3.2x10 !14 kg $ !3 ' = 3.2x10 !2 ng
# 10 kg &
3