Metric Units, scientific notation, basic conversions (dimensional analysis): 8/29—8/31/2011

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Metric Units, scientific notation, basic conversions (dimensional analysis): 8/29—8/31/2011. Biochemistry chapter 1.1-1.2, 1.5—7. Unit 2: Scientific measurements & calculations chapter 1, K. Timberlake 2009.

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### Metric Units, scientific notation, basic conversions (dimensional analysis): 8/29—8/31/2011

Biochemistry chapter 1.1-1.2, 1.5—7

Unit 2: Scientific measurements & calculationschapter 1, K. Timberlake 2009.

Learning goal: Students will understand how scientists use the metric system to report measurements, and they will be able to assess the likely error present in a measurement.

Level 2.0 Know basic terms and definitions and concepts or examples. (memorize, write definitions, identify, match, list, fill in the blank)

i. Convert between decimal numbers or fractions and exponential numbers (e.g., 1 x 10-1 or 1 x 104), and convert exponential numbers to scientific notations.

• Know the names and symbols for standard metric units of length, volume, mass, & time.
• Memorize the definitions for the metric prefixes kilo, centi, milli, and micro
• Memorize the mneumonic for the order and relative sizes of the metric prefixes, Kilo- through micro-.
Level 3.0 Know & apply information from level 2.0 to achieve the learning goal.
• Use the metric prefix mneumonic to write conversion factor equations that could be used for converting from one metric unit to any other.
• Use the metric prefix mneumonic to carry out the conversion of measurements from one metric unit to another (length  length, volume volume, timetime, massmass)
• Be able to complete one step dimensional analysis conversions for any measurements.

Level 4.0 Show greater depth of understanding than specifically taught.

• Use the metric prefix mneumonic to write in your own words—or describe with a novel diagram—a rule for using the mneumonic to convert from one metric unit to another.

ii. Be able to complete two or more step dimensional analysis conversions for any measurements, and be able to work with compound units (e.g., convert 3 miles/hr to micrometers/s)

Level 2.0 I self-assessmentScientific notation: fill in the missing cells in the table below.

Scientific notation is the form #.#...# X 10□

Decimal notation

Scientific notation

127 m

1.27 x 102 m

0.0907 l

9.07 x 10–2 l

0.000506 s

5.06 x 10–4 s

2 300 000 000 000 g

2.3 x 1012 g

King Henry Died Unexpectedly Drinking Chocolate Milk ▬ ▬ µKilo- Hecta- Deca- unit deci- centi- milli ▬ ▬ micro-

For each position separating units in the mneumonic, the size of 1 unit increases by one order of magnitude with each movement left; the size decreases by one order of magnitude with each movement right.

So

Know 1Ksneed to know #Hs (move one position right to the unknown)

How many Hs are in 1 Ks?

1 Ks = 10 Hs = 1 x 101 Hs

this means that a Ks is 10 times bigger than a Hs

How many Ks are in 1 Hs?

1 Hs = 0.1 Ks = 1 x 10-1 Ks

this means that Hs is 10 times smaller than a Ks

King Henry Died Unexpectedly Drinking Chocolate Milk ▬ ▬ µKilo- Hecta- Deca- unit deci- centi- milli ▬ ▬ micro- unknown given (answer smaller than 1, exponent of 10 negative) unknown given (answer smaller than 1, exponent of 10 negative)

? Km =1 Dm

move 2 positions left from the given value of 1 Dm, so

1 Dm = 1 x 10-2 Ks =0.01 Ks

? ml = 1 Hl

move 5 positions right from given value to unknown

1 Hl = 1 x 105 ml = 10,000 ml

King Henry Died Unexpectedly Drinking Chocolate Milk ▬ ▬ µKilo- Hecta- Deca- unit deci- centi- milli ▬ ▬ micro- unknown given (answer smaller than 1, exponent of 10 negative) unknown given (answer smaller than 1, exponent of 10 negative)Multiply the given value by the difference in size of the units!

? Km =15 Dm

move 2 positions left from given value of 1 Dm

1 Dm = 1 x 10-2 Ks =0.01 Ks

15 Dm = 15 (1 x 10-2 Ks ) = 0.15 Ks

? ml = 0.09 Hl

move 5 positions right from given value to unknown

1 Hl = 1 x 105 ml = 10,000 ml

0.09Hl=0.09(1 x 105ml)=9 x 10-2(1 x 105ml)= 9 x 103ml =9000ml

King Henry Died Unexpectedly Drinking Chocolate Milk ▬ ▬ µKilo- hecta- deca- unit deci- centi- milli ▬ ▬ micro-

Level 2.0 iii, iv self assessment

Memorize the definitions for the metric prefixes kilo, centi, milli, and micro

? Meters in one kilometer? __________

?Centiliters in one liter? ___________

?Microseconds in one second? __________

?Grams in 1 microgram? ___________

King Henry Died Unexpectedly Drinking Chocolate Milk ▬ ▬ µKilo- hecta- deca- unit deci- centi- milli ▬ ▬ micro-

Level 3.0 i self assessment

Use the metric prefix mneumonic to develop conversion factors for converting from one metric unit to any other

? Meters in 1 Hm __________

?Centiliters in one kiloliter ___________

?Microseconds in one millisecond __________

?Grams in 1 decigram ___________

King Henry Died Unexpectedly Drinking Chocolate Milk ▬ ▬ µKilo- hecta- deca- unit deci- centi- milli ▬ ▬ micro-

Level 3.0 ii self assessments

Use the metric prefix mneumonic to convert measurements from one metric unit to another

? Meters in 15 Km Hm __________

?Centiliters in 1 x 10-6 kiloliter ___________

?Milliseconds in 23 microseconds __________

?micrograms in 1 decigram ___________

King Henry Died Unexpectedly Drinking Chocolate Milk ▬ ▬ µKilo- hecta- deca- unit deci- centi- milli ▬ ▬ micro-

Level 4.0 i self-assessment

Use the metric prefix mneumonic to write in your own words—or describe with a novel diagram—a rule for using the mneumonic to convert from one metric unit to another.

______________________________________________________________________________________________________________________________________________________

If apples cost \$1.50 per kilogram, then how many kilograms can you buy if you have \$10?

Given value ______________

Given value units _______________

Needed value units _______________

Useful conversion factor (equal value) ________

Set up ______________

Level 3.0 iiiBe able to complete one step dimensional analysis conversions for any measurements.

General format for unit conversion (also called dimensional analysis)

• Given value

the originally given quantity whose units of measurement need to be converted

• Needed value

the same quantity expressed in the new units

• Giving unit
• Needed unit
• Conversion factor
• a fraction whose denominator and numerator have the same value (equivalent value), even though the units of measure are different

10 dimes = 1 \$ 1 \$/10 dimes 10 dimes/1 \$

unit conversion set up

given value unitgv/1 * equivalent value unitnv

equivalent value unitgv

example of unit conversion set up

• How many dimes should be exchanged for 15 \$?

15 \$/1 * 10 dimes/1 \$ = (15 * 10) dimes/1 = 150 dimes

Do the odd numbered problems on page 39 using the values table in the chapter. Check answers.