Metric System Be able to measure/calculate mass, volume, distance, density & temperature

Metric System• Be able to measure/calculate mass,

volume, distance, density & temperature

Measuring Length The scale on a

measuring device determines the magnitude of the uncertainty for the recorded measurement.

• Include all certain digits plus one uncertain digit in your measurement!– significant (figures)

digits (sd)

Volume/Space

• Liter (L) 1 L = 1 dm3

• Milliliter (mL) 1 mL = 1 cm3 = 1 cc

• Microliter (L) 1 L = 1 mm3

Measuring Volume

• Note the type of liquid• Indicate which kind of

meniscus it is (concave or convex)– Concave: read the bottom of

the meniscus (WATER)– Convex: read the top of the

meniscus (MERCURY)

• Include all certain digits plus one uncertain digit in your measurement!– sd

Measuring Mass• Check that the scale

is TARED prior to placing anything on it.

• Include all certain digits plus one uncertain digit in your measurement!– Sd– Digital balances give

all sd in readout!

Mass/Weight

• A gram is defined as the mass of 1 ml of water at 4˚C. Therefore, water has a density of 1 g/mL at 4˚C.

Converting between Measurement Units

Conversions 453.6 graham crackers = 1 pound cake

2000 mockingbirds = 2 kilomockingbirds

Distance Conversion

It is experimentally determined that 1 inch equals 2.54 cm, or 1 cm equals 0.394 inch

Density• The ratio of the mass of an object to it’s

volume is known as DENSITY

• Density = Mass/Volume

• D = m/V

• Two common density units (used in Chemistry) are g/mL and g/cm3

Density

Both of these items have a mass of 23 grams, but they have very different volumes; therefore, their densities are different as well.

Density comparison

The penny is less dense than the mercury it floats on.

Densities of Common materials

The use of the concentration unit milligrams per deciliter (mg/dL) is

common in clinical laboratory reports dealing with the composition of human

body fluids.

Temperature - the degree of hotness or coldness

• Fahrenheit (˚F)• Celsius (˚C)• Kelvin (K)

• K = ˚C + 273• ˚C = K - 273• ˚C = (˚F - 32 )/1.8• ˚F = (1.8 x ˚C) + 32

Relationships among temperature scales

The relationships among the Celsius, Kelvin, and Fahrenheit temperature scales are determined by the degree sizes and the reference point values.

Metric System Review

Type of Measurement

Base Unit

Prefixes Conversion factor examples

Mass Gram (g) Kilo (1000x larger)

Centi (100x smaller)

Milli (1000x smaller)

Distance Meter (m)

“

Volume Liter (L) “

DensityGrams/milliter

(g/mL)(g/cm3)

Temperature ˚C

K

K = ˚C + 273

˚C = K - 273

Significant Digits in Measurements

• Measurements must be reported with the digits that actually have meaning (significance to the measurement)

• Example: Your height is measured with a metric ruler and the top of your head lies about half-way between 171 and 172 cm. How would you report your height?

• For more help on SD, see Ch.1, Section 1.5 AND Appendix A (pg.A-2) in your textbook.

Rule for measuring SD!

Report all digits which can be measured accurately (certain digits) plus one digit which is guessed at (uncertain digit)!

Rules for Determining Significant

Figures (in reported #s)

Rules for determining Significant Digits in Reported Numbers

• 1. If a number >1 and a decimal is shown, all digits are SIGNIFICANT.

• 2. If a number >1 and NO decimal is shown, ending zeros (place holders) are NOT significant (Exception: Bar over a Zero makes IT and all digits to its left significant).

• 3. If a number is <1, leading zeros & place holders are NOT significant.

Determining SD as a result of Calculations

• It is assumed you know how to add, subtract, multiply and divide

• You must be able to express an answer to a calculation to the correct number of significant digits and with the appropriate unit(s).

When do you need to “round” numbers?

The digital readout on an electronic calculator usually shows more digits than are needed.

Math Rules• Adding and Subtracting: the answer

must be reported to the same number of decimal places as that of the term with the least number of decimal places

• Multiplying and Dividing: the answer must be reported as having the same number of significant digits as the measurement with the fewest significant digits

MEASUREMENTS

• Scientific measurements should be both accurate and precise

• ACCURACY is how close a measurement is to the real/true/literature value– Which is more accurate?

• 3.00 g OR 3.000 g Why?

• PRECISION – SD from instrument– Reproducibility of measurement

ERROR

• Absolute error - amount of difference between your measurement and the actual measurement

• Percent error - use formula:

Converting between Measurement Units

Problem Solving & Dimensional Analysis

• Identify the Unknown (& unit)• Identify what is known/given

– Write it down!

• Develop/use an equation to solve– Conversion factors from defined relationships

have infinite significant digits (figures)– Conversion factors from measured relationships

have significant digits (sd) based on precision

• Perform the calculations– Be aware of sig figs (sd) and units– Cancel units as you go

• Check your work!!

EXAMPLE• A patient is prescribed 1.25 g of

amoxicillan, which is available in 250-mg tablets. How many tablets are needed?

•Identify the Unknown (& unit)•Identify what is known/given

–Write it down!•Develop/use an equation to solve•Perform the calculations

–Be aware of sig figs and units–Cancel units as you go

•Check your work!!

EXAMPLE• How many milliliters of Children’s

Motrin (100 mg of ibuprofen per 5 mL) are needed to give a child a dose of 160 mg?





When the human body is exposed to extreme cold, hypothermia can result and the body’s temperature can drop to 28.5˚C. Convert this temperature to K and ˚F.

• Identify the Unknown (& unit)

• Identify what is known/given– Write it down!

• Develop/use an equation to solve

• Perform the calculations– Be aware of sig figs and

units– Cancel units as you go

• Check your work!!

Calculate the mass in grams of 10.0 mL of diethyl ether, an anesthetic that has a density of 0.713 g/mL.





Calculate the volume of 100. G of coconut oil, which has a density of 0.92 g/mL. How many liters does this correspond to?





Determine the density of a 5.050 g sample of metal. When placed in 25.50 mL of water, the metal sample causes the water level to rise to 26.02 mL. Using your lab book, what is the likely identity of the metal?





Review• States & Changes of Matter• Metric prefixes you must know

• kilo (k)• centi (c)• milli (m)• micro ()

• Significant digits (sd)• Measured (all certain digits + one guessed digit)• Reported (be able to use the 3 rules to id sd in #)

• Math rules• + & - vs. x & /

• Scientific notation• Two terms

– 1st: contains ALL sd– 2nd: IDs decimal places

• Density (D = m/v): be able to solve for any (of 3) variables

• Temperature• C & K

• Conversions

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Metric System Be able to measure/calculate mass, volume, distance, density & temperature