Measurement

1
Measurement

• 2005 - 2006

2
Units of Measurement

• There are two different systems of measurement
  used by scientists and health professionals
• Metric System
• International System of Units (SI)
• A more simplified form of the metric system that
  has seven base units as its foundation.
• Adopted in 1960 by the National Bureau of
  Standards
• The metric and SI systems are decimal systems, in
  which prefixes are used to indicate fractions and
  multiples of ten.
• The same prefixes are used with all units of
  measurement.

3
Units of Measurement

• Seven Base Units of the SI System
• Length Meter (m)
• Mass Kilogram (kg) Metric Gram (g)
• Time Second (s)
• Electric Current Ampere (A)
• Temperature Kelvin (K) Metric Celsius (C)
• Luminous Intensity Candela (cd)
• Amount of Substance Mole (mol)
• The degree Celsius is the common unit for the
  measurement of temperature.
• Technical calculations involving temperature
  must, however, use kelvin.

4
Units of Measurement

• Why have a standardized system of units?
• To provide uniformity in measurements between
  different countries in the world.
• Example
• Prior to the National Bureau of Standards, at
  least 50 different distances had been used as 1
  foot in measuring land within New York City.
• Thus the size of a 100-ft by 200-ft lot in NYC
  depended on the generosity of the seller and did
  not necessarily represent the expected
  dimensions.
• In this class we will use metric units and
  introduce some of the SI units that are in use
  today.

5
Scientific Notation

• In science we use numbers that are very, very
  small to measure things as tiny as the width of a
  human hair (.000 008-m), or things that are even
  smaller.
• Or perhaps we want to number the number of hairs
  on the average scalp (100 000 hairs).
• In both measurements, it is convenient to write
  the numbers in scientific notation (8 10-6 m
  and 1 105 hairs).

6
Scientific Notation

• When a number is written in scientific notation,
  there are two parts, a coefficient and a power of
  10.
• Example
• 2400 2.4 103
• The value 2.4 is the coefficient and 103 is the
  power of 10.
• The coefficient was determined by moving the
  decimal point to the left to give a number
  between 1 and 10.
• Counting the number of places (3) we moved the
  decimal gives the power of 10.
• For a large number, the power of 10 is always
  positive.
• When a small number is written in scientific
  notation, the power of 10 will be negative.

7
Scientific Notation

• Examples
• Write the following measurements in scientific
  notation
• 350 g
• 0.000 16 L
• 5 220 000 m
• 425 000 m
• 0.000 000 8 g
• 0.0086 g

8
Scientific Notation

• Examples
• Write the following as standard numbers
• 2.85 102 L
• 7.2 10-3 m
• 2.4 105 g
• 8.25 10-2 mol
• 4 106 g
• 3.6 10-5 L

9
Measured and Exact Numbers

• Measured numbers are the numbers you obtain when
  you measure a quantity such as your height,
  weight, or temperature.
• Example
• Suppose you are going to measure the lengths of
  the following objects

10
Measured and Exact Numbers

• By observing the lines on the scale, you
  determine the measurement for each object.
• To report the length, you would first read the
  numerical value of the marked line.
• Finally, you would make an estimation of the
  distance between the smallest marked lines.
• The estimated value is the final digit in a
  measured number.
• An estimation is made by visually breaking up the
  space between the smallest marked lines, usually
  into tenths.

11
Measured and Exact Numbers

• For example, in the top figure, the end of the
  object falls between the lines marked 4-cm and
  5-cm.
• That means that the length is 4-cm plus an
  estimated digit.
• If you estimate that the end is halfway between
  4-cm and 5-cm, you would report its length as
  4.5-cm.
• However, someone else might report its length as
  4.4-cm.
• The last digit in measured numbers will differ
  because people do not estimate in the same way.

12
Measured and Exact Numbers

• The ruler shown in the bottom figure is marked
  with lines at 0.1-cm.
• With this ruler, you can estimate to the 0.01-cm
  place.
• Perhaps you would report the length of the object
  as 4.55 cm, while someone else may report its
  length as 4.56-cm.
• Does this mean that one of the measurements is
  wrong?
• No, Both results are acceptable.

13
Measured and Exact Numbers

• Because there are variations in estimation, there
  is always some uncertainty in every measurement.
• Sometimes a measurement end right on a marked
  line.
• In order to indicate the uncertainty of the
  measurement, a zero is written as the estimated
  figure.
• The zero in the uncertainty place indicates that
  the measurement was not above or below the value
  of that line.

14
Measured and Exact Numbers

• Exact numbers are numbers we obtain by counting
  items or from a definition that compares two
  units in the same measuring system.
• Example
• Suppose a friend asks you to tell her the number
  of coats in your closet or the number of bicycles
  in your garage or the number of classes you are
  taking in school.
• To do this you must have counted the items.
• It was not necessary for you to use any type of
  measuring tool.

15
Measured and Exact Numbers

• Example
• Identify the following as an exact or a measured
  number
• Number of eggs in a 3-egg omelet.
• Amount of coffee needed to make 10-cup pot of
  coffee.
• Number of tea bags needed to make a pot of tea.
• Amount of sugar needed to sweeten the coffee or
  tea.

16
Significant Figures

• When we work in a medical environment or in a
  laboratory, it is important to make measurements
  that are accurate and that can be duplicated.
• A measurement is accurate when it is close to the
  real size or actual value of what we are
  measuring.
• That means we need to be careful when we
  determine a patients temperature or take a blood
  pressure.
• It is also important to use a measuring
  instrument that is properly adjusted.
• Using a measuring device that is not in good
  working order will not give an accurate result
  even with careful measuring.

17
Significant Figures

• A measurement is precise if it can be repeated
  many times with results that are very close in
  value to each other.
• Example
• Suppose that four students measure your height as
  152.3-cm, 152.4-cm, 152.1-cm, and 152.3-cm.
• Your actual height is 152.3-cm.
• Are the measurements accurate? Are they precise?

18
Significant Figures

• Example
• The standard diameter for a large pizza at the
  Pizza Shack is 14-inches. However, the new pizza
  maker has prepared four pizzas that are each
  10-inches in diameter.
• Is the size of the pizzas accurate? Why?
• Is the size of the pizzas precise? Why?
• What should be the size of the large pizzas to be
  both accurate and precise?

19
Significant Figures

• In measured numbers, the significant figures are
  all the reported numbers including the estimated
  digit.
• When we do calculations, we will need to count
  the significant figures in each of the measured
  numbers used in the calculations.
• All nonzero numbers are counted as significant
  figures.
• Zeros may or may not be significant depending on
  their position in a number.

20
Significant Figures

• Rules for Significant Figures
• A number is a significant figure if it is
• A nonzero digit.
• Ex 4.5-g 2 sig. figs.
• Ex 122.35-m 5 sig. figs.
• b. A zero between nonzero digits.
• Ex 205-m 3 sig. figs.
• Ex 5.082-kg 4 sig. figs.
• A zero at the end of a decimal number.
• Ex 50.-L 2 sig. figs.
• Ex 25.0-C 3 sig. figs.
• d. Any digit in the coefficient of a number
  written in scientific notation.
• Ex 4.0 105-m 2 sig. figs.
• Ex 5.70 10-3-g 3 sig. figs.

21
Significant Figures

• 2. A number is not significant is it is
• A zero at the beginning of a decimal number.
• Ex 0.0004-lb 1 sig. fig.
• Ex 0.075-m 2 sig. figs.
• b. A zero used as a placeholder in a large number
  without a decimal point.
• Ex 850 000-m 2 sig. figs.
• Ex 1 250 000-people 3 sig. figs.

22
Significant Figures

• Example
• Identify each of the following numbers as
  measured or exact give the number of significant
  figures in each of the measured numbers.
• 42.2-g
• 3-eggs
• 0.0005-cm
• 450,000-km
• 9-planets

23
Significant Figures

• In science and medicine, we measure things the
  length of a bacterium, the volume of medication,
  the mass of cholesterol in a blood sample.
• The number from these measurements are often used
  in calculations.
• However, calculations cannot change the precision
  of a measured number.
• Therefore, we report a calculated answer that
  reflects the precision of the original
  measurements.

24
Significant Figures

• Rounding Off
• If we calculate the area of a carpet that
  measures 5.5-m by 3.5-m, we obtain the number
  19.25 as the square meters in the area (5.5-m
  3.5-m 19.25-m2).
• However, all four digits cannot be significant
  because the answer cannot be more precise than
  the measured numbers used.
• Because each of the measurement numbers has just
  two sig. figs., the calculated result must be
  round off to give an answer that also has two
  significant figures 19-m2.

25
Significant Figures

• Rules for Rounding Off
• If the first digit to be dropped in 4 or less, it
  and all the following digits are simply dropped
  from the number.
• Examples
• Round 8.4234 to 3 sig. figs.
• Round to 2 sig. figs.
• If the first digit to be dropped is 5 or greater,
  the last retained digit of the number is
  increased by 1.
• Examples
• Round 14.780 to 3 sig. figs.
• Round to 2 sig. figs.

26
Significant Figures

• Examples
• Round each of the following numbers to 3
  significant figures
• 35.7823-m
• 0.002627-L
• 3826.8-g
• 1.2836-kg
• Now round them all to 2 sig. figs.

27
Significant Figures

• Multiplication and Division
• In multiplication and division, the final answer
  is written so it has the same number of digits as
  the measurement with the fewest significant
  figures.
• Examples
• Multiply the following
• 24.65 0.67
• What is the answer rounded to the correct number
  of sig. figs.?
• Divide the following
• (2.85 67.4)/4.39
• What is the answer rounded to the correct number
  of sig. figs.?

28
Significant Figures

• Addition and Subtraction
• In addition and subtraction, the answer is
  written so it has the same number of decimal
  places as the measurement having the fewest
  decimal places.
• Examples
• Add the following
• 2.045 34.1
• What is the answer rounded to the correct number
  of sig. figs.?
• Subtract the following
• 255 175.65
• What is the answer rounded to the correct number
  of sig. figs.?

29
Significant Figures

• Adding Significant Zeros
• Sometimes, a calculator displays a small whole
  number.
• To give an answer with the correct number of sig.
  figs., significant zeros are written after the
  calculator result.
• Example
• Divide the following
• 8.00/2.00
• What is the answer rounded to the correct number
  of sig. figs.?
• Did you have to add any sig. zeros to get the
  correct answer?

30
Significant Figures

• Perform the following calculations and give the
  answer with the correct number of decimal places
• 27.8-cm 0.235-cm
• 104.45-mL 0.838-mL 46-mL
• 153.247-g 14.82-g
• 4.259-L 3.8-L
• 56.8 0.37
• 71.4/11
• (2.075 0.585)/(8.42 0.0045)
• 25.0/5.00

31
SI and Metric Prefixes

• The special feature of the metric system of units
  is that a prefix can be attached to any unit to
  increase or decrease its size by some factor of
  10.
• Examples
• In the daily values of nutrients label on food,
  the prefixes milli (1/1000) and micro (1/1000000)
  are used to make the smaller units, milligram
  (mg) and microgram (µg).
• The prefix centi is like cents in a dollar. One
  cent would be a centidollar or 1/100 of a dollar.
  That also means that one dollar is the same as
  100 cents.
• The prefix deci is like dimes in a dollar. One
  dime would be a decidollar or 1/10 of a dollar.
  That also means that one dollar is the same as 10
  dimes.

32
SI and Metric Prefixes

• The relationship of a unit to its base unit can
  be expressed by replacing the prefix with its
  numerical value.
• Examples
• When the prefix kilo in kilometer is replaced
  with its value of 1000, we find that a kilometer
  is equal to 1000 meters.
• 1 kilometer 1000 meters
• 1 kiloliter 1000 liters
• 1 kilogram 1000 grams

33
SI and Metric Prefixes

• Examples
• Fill in the blanks with the correct numerical
  value
• Kilogram __________ grams
• Millisecond __________ seconds
• Deciliter __________ liters
• Write the correct prefix in the blanks
• 1000000 seconds __________seconds
• 0.01 meters __________meters
• 1000000000 grams __________grams

34
Measuring Volume

• Volume of 1-liter (1-L) or smaller are common in
  the health services.
• When a liter is divided into 10 equal portions,
  each portion is a deciliter (dL).
• There are 10-dL in 1-L.
• Laboratory results for blood work are often
  reported in deciliters.
• Example
• Cholesterols typical range in blood is from 105
  to 250-mg/dL.
• Total proteins typical range in blood is from 6.0
  to 8.0-g/dL.

35
Measuring Volume

• When a liter is divided into a thousand parts,
  each of the smaller volumes is called a
  milliliter (mL).
• In a 1-L container of physiological saline, there
  are 1000-mL of solution.
• Volume Equalities
• 1-L 10-dL
• 1-L 1000-mL
• 1-dL 100-mL

36
Measuring Volume

• The cubic centimeter (cm3 or cc) is the volume of
  a cube whose dimensions are 1-cm on each side.
• A cubic centimeter has the same volume as a
  milliliter, and the units are often used
  interchangeably.
• 1-cm3 1-cc 1-mL
• When you see 1-cm, you are reading about length
  when you see 1-cc or 1-cm3 or 1-mL, you are
  reading about volume.

37
Measuring Mass

• When you get a physical examination, your mass is
  recorded in kilograms (kg), whereas the results
  of your laboratory tests are reported in grams
  (g), milligrams (mg), or micrograms (µg).
• Mass Equalities
• 1-kg 1000-g
• 1-g 1000-mg
• 1-mg 1000-µg

38
Problem Solving Using Conversion Factors

• Many problems in science and the health services
  require a change of units.
• You make changes in units everyday.
• Example
• Suppose you spent 2.0-hours on your homework, and
  someone asked you haw many minutes that was.
• To do this problem, the equality is written in
  the form of a fraction called a conversion
  factor.
• One of the quantities is the numerator, and the
  other is the denominator.
• Numerator/Denominator
• 60-min/1-hr
• 1-hr/60-min
• Two factors are always possible from any equality.

39
Problem Solving Using Conversion Factors

• These factors are read as 60 minutes per 1
  hour, and 1 hour per 60 minutes.
• The term per means divide.
• The usefulness of conversion factors is enhanced
  by the fact that we can turn a conversion factor
  over and use its inverse.

40
Problem Solving Using Conversion Factors

• Examples
• Write conversion factors for the relationship for
  the following pairs of units
• Milligrams and grams
• Minutes and hours
• Quarts and milliliters
• Inches and centimeters
• Feet and miles

41
Problem Solving Using Conversion Factors

• The process of problem solving in science
  requires you to convert a quantity given
  initially in one unit to the same quantity in
  different units.
• Using one or more conversion factors accomplishes
  this conversion.
• Quantity (Initial unit) Conversion Factor
  Same Quantity (New unit)

42
Problem Solving Using Conversion Factors

• Example
• Suppose you have a patient with a weight of
  165-lbs. In order to give a medication, you need
  to know the patients mass in kilograms.
• Given 165-lbs
• Units Plan 1bs ? kg
• Relationship 1-kg 2.20 lbs
• Conversion Factors 1-kg/2.20-lbs and
  2.20-lbs/1-kg
• Now, multiply the given by the conversion factor
  that has the unit lbs in the denominator because
  that will cancel out the given unit in the
  numerator.
• Problem Setup
• 165-lbs (1-kg/2.20-lbs)
• Take a look at the way the units cancel
• The units that you want in the answer is the one
  that remains after all the other units have
  canceled out.
• This is a helpful way to check a problem.
• If the units do not cancel, you know there is an
  error in the setup.

43
Problem Solving Using Conversion Factors

• Examples
• The Daily Value (DV) for sodium is 2400-mg. How
  many grams of sodium is that?
• A can containing 473-mL of frozen orange juice is
  mixed with 1415-mL of water. How many liters of
  orange juice were prepared?

44
Problem Solving Using Conversion Factors

• In many problems you will need two or more steps
  in your unit plan.
• Then two or more conversion factors will be
  required.
• In setting up the problem, one factor follows the
  other.
• Each factor is arranged to cancel the preceding
  unit until you obtain the desired unit.

45
Problem Solving Using Conversion Factors

• Example
• A recipe for salsa requires 3.0 cups of tomato
  sauce. If only metric measures are available, how
  many milliliters of tomato sauce are needed?
  (There are only 4 cups in 1 quart.)
• Given 3.0 cups
• Unit Plan cups ? quarts ? milliliters
• Relationship 1-qt 4 cups and 1 qt 946-mL
• Conversion Factors 1-qt/4-cups and 4-cups/1-qt
• 1-qt/946-mL and 946-mL/1-qt
• Problem Setup
• 3.0-cups (1-qt/4-cups) (946-mL/1-qt)

46
Problem Solving Using Conversion Factors

• Example
• One medium bran muffin contains 4.2-g of fiber.
  How many ounces (oz) of fiber are obtained by
  eating 3 bran muffins, if 1-lb 16-oz?

47
Clinical Calculations Using Conversion Factors

• Conversion factors are also used for calculating
  medications.
• Example
• If an antibiotic is available in 5-mg tablets,
  the dosage can be written as a conversion factor,
  5-mg/1-tablet.
• In many hospitals, the apothecary unit of grains
  (gr) is still in use there are 65-mg in 1-gr.
• When you do a medication problem, you often start
  with a doctors order that contains the quantity
  to give the patient.
• The medication dosage is used as a conversion
  factor.

48
Clinical Calculations Using Conversion Factors

• Example
• Synthyroid is used as a replacement or supplement
  therapy for diminished thyroid function. A dosage
  of 0.200-mg is prescribed with tablets that
  contain 50-µg Synthyroid. How many tablets are
  required to provide the prescribed medication?
• Given 0.200-mg
• Unit Plan mg ? µg ? tablets
• Relationships 1-mg 1000-µg and 1-tablet
  50-µg
• Conversion Factors 1-mg/1000-µg and 1000-µg/1-mg
• 1-tablet/50-µg and 50-µg/1-tablet
• Problem Setup
• 0.200-mg (1000-µg/1-mg) (1-tablet/50-µg)

49
Clinical Calculations Using Conversion Factors

• Examples
• An antibiotic dosage of 500-mg is ordered. If the
  antibiotic is supplied in liquid form as 250-mg
  in 5.0-mL, how many mL would be given?
• Some important functions of calcium in the body
  are bone formation, muscle contraction, and blood
  coagulation. For an adult, the normal range for
  serum calcium is 8.7 10.2-mg/dL. A calcium
  deficiency (hypocalcemia) can cause muscle
  spasms, cramps, and convulsions. Determine
  whether a calcium level falls within the normal
  range is a 2.0-mL serum sample from a patient
  contains 180-µg of calcium.
• A patient has a serum calcium of 0.050-g/L. Does
  this patient have a normal calcium, hypocalemia,
  or hypercalcemia (low or high calcium level in
  the blood)?

50
Using Percents as Conversion Factors

• Sometimes percents are given in a problem.
• To work with a percent, it is convenient to write
  it as a conversion factors.
• To do this, we choose units from the problem to
  express the numerical relationship of the part to
  100 parts of the whole.
• Example
• An athlete might have 18 body fat by weight
• We can use a choice of units for weight or mass
  to write the following conversion factors
• 18-kg body fat/100-kg body mass
• 18-lbs body fat/100-lbs body weight

51
Using Percents as Conversion Factors

• Example
• How many kilograms of body fat are in a marathon
  runner with a total body mass of 48-kg if the
  marathon runner has 18 body fat by weight.
• 48-kg body mass (18-kg body fat/100-kg body
  mass)
• If the problem asks about the pounds of body fat
  in a dancer weighing 126-lbs, we would state the
  factor in lbs of body fat.
• 126-lbs body weight (18-lbs body fat/100-lbs
  body weight)

52
Using Percents as Conversion Factors

• Examples
• A wine contains 13 alcohol by volume. How many
  milliliters of alcohol are contained in a glass
  containing 125-mL of the wine?
• There are 85 students in a science class. On the
  last test, 20 received grades of A. How many As
  were earned on the test?

53
Density

• Density is the ratio of mass to volume in an
  object.
• Density (Mass of Substance/Volume of Substance)
• In the metric system, the densities of solids and
  liquids are usually expressed as grams per cubic
  centimeter (g/cm3) or grams per milliliter
  (g/mL).
• The density of gases is usually stated as grams
  per liter (g/L).

54
Density

• Examples
• A 50.0-mL sample of buttermilk has a mass of
  56.0-g. What is the density of the buttermilk?
• A copper sample has a mass of 44.65-g and a
  volume of 5.0-cm3. What is the density of copper,
  expressed as grams per cubic centimeter (g/cm3)?
• A lead weight used in the belt of a scuba diver
  has a mass of 226-g. When the weight is carefully
  placed in a graduated cylinder containing
  200.0-mL of water, the water level rises to
  220.0-mL. What is the density of the lead weight
  (g/mL)?

55
Specific Gravity

• Specific gravity (sp gr) is a ratio between the
  density of a substance and the density of water.
• Specific gravity is calculated by dividing the
  density of a sample by the density of water.
• Specific Gravity Density of Sample/Density of
  Water
• We will use the metric value of 1.00-g/mL for the
  density of water (constant).
• A substance with a specific gravity of 1.00 has
  the same density as water.
• A substance with a specific gravity of 3.00 is
  three times as dense as water.

56
Specific Gravity

• In calculations for specific gravity, the units
  of density must match.
• Then all the units cancel to leave only a number.
• Specific gravity is one of the few unitless
  values you will encounter in science.
• An instrument called a hydrometer is often used
  to measure the specific gravity of fluids such as
  battery fluid or a sample of urine.

57
Specific Gravity

• Examples
• What is the specific gravity of coconut oil that
  has a density of 0.925-g/mL?
• What is the specific gravity of ice if 35.0-g of
  ice has a volume of 38.2-mL?
• John took 2.0 teaspoons (tsp) of cough syrup (sp
  gr 1.20) for a presistent cough. If there are
  5.0-mL in 1-tsp, what was the mass (in grams) of
  the cough syrup?
• An ebony carving has a mass of 275-g. If ebony
  has a specific gravity of 1.33, what is the
  volume of the carving?

58
Temperature

• When we take the temperature of a substance, we
  are measuring the intensity of heat.
• Temperature tells us the direction that heat will
  flow between two substances.
• Heat always flows from a substance with a higher
  temperature to a substance with a lower
  temperature until the temperatures of both are
  the same.
• We use thermometers to determine how hot or
  cold a substance is.
• When a thermometer is placed in a substance, the
  heat flow causes the liquid in the thermometer
  (alcohol or mercury) to expand or contract.

59
Temperature

• Temperatures in science, and in most of the
  world, are measured and reported in Celsius (C).
• In the United States, everyday temperatures are
  commonly reported in Fahrenheit (F) units.
• On the Celsius and Fahrenheit scales, the
  temperatures of melting ice and boiling water are
  used as reference points.
• On the Celsius scale, the freezing point of water
  is defined as 0C, and the boiling point as
  100C.
• On a Fahrenheit scale, water freezes at 32F and
  boils at 212F.

60
Temperature

• On each scale, the temperature difference between
  freezing and boiling is divided into smaller
  units, or degrees.
• On the Celsius scale, there are 100 units between
  freezing and boiling of water compared to 180
  units on the Fahrenheit scale.
• That makes a Celsius unit almost twice the size
  of a Fahrenheit degree
• 1C 1.8F

61
Temperature

• In science or in a hospital, you will measure
  temperatures in Celsius units.
• To convert between Celsius and Fahrenheit, use
  the following conversion factors
• F 1.8(C) 32
• C (F 32)/1.8

62
Temperature

• Examples
• While traveling in China, you discover that your
  temperature is 38.2C. What is your temperature
  measured with a Fahrenheit thermometer?
• When making ice cream, you use rock salt to chill
  the mixture. If the temperature drops to -11C,
  what is it in Fahrenheit?
• You are going to cook a turkey at 325F. If you
  use an oven with Celsius settings, at what
  temperature should you set it?
• Your patient has a temperature of 103.6F. What
  is this temperature on a Celsius thermometer?

63
Temperature

• Scientists tell use that the coldest temperature
  possible is -273.15C.
• On the Kelvin scale, this temperature, called
  absolute zero, has the value of 0 Kelvin (0 K).
• Units on the Kelvin scale are called kelvins (K)
  no degree symbol is used.
• Because there are no lower temperatures, the
  Kelvin scale has no negative numbers.
• Between the freezing and boiling points of water,
  there are 100 kelvins, which makes a kelvin equal
  in size to a Celsius unit.
• 1 K 1C
• To convert between Celsius and Kelvin, use the
  following conversion factor
• K C 273.15

64
Temperature

• Examples
• What is a normal body temperature of 37C on the
  Kelvin scale?
• You are cooking a pizza at 375F. What is that
  temperature in kelvins?
• In a cryogenic laboratory, a technician freezes a
  sample using liquid nitrogen at 77 K. What is the
  temperature in C?
• On the planet Mercury, the average night
  temperature is 13 K, and the average day
  temperature is 683 K. What are these temperatures
  in Celsius degrees?