2.4 chem

General, Organic, and Biological Chemistry: Structures of Life

Chapter 2: Chemistry and Measurements

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2.4 Prefixes and Equalities

  • Application Context: An ophthalmologist uses a retinal camera to photograph the retina, demonstrating the importance of measurements in healthcare.

  • Learning Goal: Utilize numerical values of prefixes to establish a metric equality.

Prefixes in the Metric System

  • Definition: The metric system allows the addition of prefixes to base units to modify their size by a factor of ten.

  • Examples of Prefixes:

    • milli () and micro () are used to create smaller units.

Metric and SI Prefixes (1 of 2)

  • Prefixes that increase the size of units:

    • Peta (P)

      • Numerical Value: 1,000,000,000,000,000

      • Scientific Notation: 1imes10151 imes 10^{15}

      • Equality: 1extPg=1imes1015extg1 ext{ Pg} = 1 imes 10^{15} ext{ g} ; 1extg=1imes10−15extPg1 ext{ g} = 1 imes 10^{-15} ext{ Pg}

    • Tera (T)

      • Numerical Value: 1,000,000,000,000

      • Scientific Notation: 1imes10121 imes 10^{12}

      • Equality: 1extTs=1imes1012exts1 ext{ Ts} = 1 imes 10^{12} ext{ s} ; 1exts=1imes10−12extTs1 ext{ s} = 1 imes 10^{-12} ext{ Ts}

    • Giga (G)

      • Numerical Value: 1,000,000,000

      • Scientific Notation: 1imes1091 imes 10^{9}

      • Equality: 1extGm=1imes109extm1 ext{ Gm} = 1 imes 10^{9} ext{ m} ; 1extm=1imes10−9extGm1 ext{ m} = 1 imes 10^{-9} ext{ Gm}

    • Mega (M)

      • Numerical Value: 1,000,000

      • Scientific Notation: 1imes1061 imes 10^{6}

      • Equality: 1extmg=1imes106extg1 ext{ mg} = 1 imes 10^{6} ext{ g} ; 1extg=1imes10−6extmg1 ext{ g} = 1 imes 10^{-6} ext{ mg}

    • Kilo (k)

      • Numerical Value: 1,000

      • Scientific Notation: 1imes1031 imes 10^{3}

      • Equality: 1extkm=1imes103extm1 ext{ km} = 1 imes 10^{3} ext{ m} ; 1extm=1imes10−3extkm1 ext{ m} = 1 imes 10^{-3} ext{ km}

    • Deci (d)

      • Numerical Value: 0.1

      • Scientific Notation: 1imes10−11 imes 10^{-1}

      • Equality: 1extdL=1imes10−1extL1 ext{ dL} = 1 imes 10^{-1} ext{ L} ; 1extL=10extdL1 ext{ L} = 10 ext{ dL}

Metric and SI Prefixes (2 of 2)

  • Prefixes that decrease the size of units:

    • Centi (c)

      • Numerical Value: 0.01

      • Scientific Notation: 1imes10−21 imes 10^{-2}

      • Equality: 1extcm=1imes10−2extm1 ext{ cm} = 1 imes 10^{-2} ext{ m} ; 1extm=100extcm1 ext{ m} = 100 ext{ cm}

    • Milli (m)

      • Numerical Value: 0.001

      • Scientific Notation: 1imes10−31 imes 10^{-3}

      • Equality: 1extms=1imes10−3exts1 ext{ ms} = 1 imes 10^{-3} ext{ s} ; 1exts=1imes103extms1 ext{ s} = 1 imes 10^{3} ext{ ms}

    • Micro ()

      • Numerical Value: 0.000001

      • Scientific Notation: 1imes10−61 imes 10^{-6}

      • Equality: 1extµg=1imes10−6extg1 ext{ µg} = 1 imes 10^{-6} ext{ g} ; 1extg=1imes106extµg1 ext{ g} = 1 imes 10^{6} ext{ µg}

    • Nano (n)

      • Numerical Value: 0.000000001

      • Scientific Notation: 1imes10−91 imes 10^{-9}

      • Equality: 1extnm=1imes10−9extm1 ext{ nm} = 1 imes 10^{-9} ext{ m} ; 1extm=1imes109extnm1 ext{ m} = 1 imes 10^{9} ext{ nm}

    • Pico (p)

      • Numerical Value: 0.000000000001

      • Scientific Notation: 1imes10−121 imes 10^{-12}

      • Equality: 1extps=1imes10−12exts1 ext{ ps} = 1 imes 10^{-12} ext{ s} ; 1exts=1imes1012extps1 ext{ s} = 1 imes 10^{12} ext{ ps}

    • Femto (f)

      • Numerical Value: 0.000000000000001

      • Scientific Notation: 1imes10−151 imes 10^{-15}

      • Equality: 1extfs=1imes10−15exts1 ext{ fs} = 1 imes 10^{-15} ext{ s} ; 1exts=1imes1015extfs1 ext{ s} = 1 imes 10^{15} ext{ fs}

    • Notation in Medicine: The abbreviation "mc" is often used for micro to prevent medication errors due to misreading the symbol.

Prefixes and Equalities

  • Expression of Relationship: The relationship of a prefix to a unit can be shown by substituting the prefix with its numerical value.

    • Example: The prefix "kilo" in "kilometer" can be replaced with 1000, thus establishing the equality: 1extkm=1000extm1 ext{ km} = 1000 ext{ m}.

Daily Values for Selected Nutrients

  • The U.S. Food and Drug Administration utilizes metric prefixes to present daily nutrient recommendations.

    • Table 2.4: Daily Values (DV) for Selected Nutrients:

    • Calcium: 1.0 g

    • Copper: 2 mg

    • Iodine: 150 μg (150 mCg)

    • Iron: 18 mg

    • Magnesium: 400 mg

    • Niacin: 20 mg

    • Phosphorus: 800 mg

    • Potassium: 3.5 g

    • Selenium: 70 μg (70 mCg)

    • Sodium: 2.4 g

    • Zinc: 15 mg

Learning Check 1

  • Task: Fill in the blanks with the correct prefix:

    • A.

    • B.

    • C.

Solution 1

  • Answer Key:

    • A: The prefix for 1000 is "kilo"; therefore, 1000extm=1extkm1000 ext{ m} = 1 ext{ km}.

    • B:

    • C: The prefix for 0.01 is "centi"; therefore, 0.01extm=1extcm0.01 ext{ m} = 1 ext{ cm}.

Measuring Length

  • An ophthalmologist measures the diameter of the retina in centimeters (cm), while a surgeon measures nerve length in millimeters (mm).

  • Equalities: Different units can describe the same length.

Measuring Volume (1 of 2)

  • In health sciences, volumes of 1 L or less are common. When 1 liter is divided into 10 portions, each is called a deciliter (dL).

Measuring Volume (2 of 2)

  • Table 2.6: Normal Laboratory Test Values for Substances in Blood:

    • Albumin: 3.5–5.4 g/dL

    • Ammonia: 20 to 70 μg/dL

    • Calcium: 8.5–10.5 mg/dL

    • Cholesterol: 105–250 mg/dL

    • Iron (male): 80 to 160 μg/dL

    • Protein (total): 6.0–8.5 g/dL

The Cubic Centimeter (1 of 2)

  • A cubic centimeter (cc) is the volume of a cube with dimensions of 1 cm on each side.

    • Note: A cubic centimeter is equivalent to a milliliter (mL), and the two units are often used interchangeably.

  • Example: A plastic intravenous fluid container holds 1000 mL.

The Cubic Centimeter (2 of 2)

  • Volume Calculation: A cube with dimensions 10 cm × 10 cm × 10 cm results in:

    • Volume = 10extcmimes10extcmimes10extcm=1000extcm3=1000extmL=1extL10 ext{ cm} imes 10 ext{ cm} imes 10 ext{ cm} = 1000 ext{ cm}^3 = 1000 ext{ mL} = 1 ext{ L}.

  • Volume of 1 cm³ cube = 1 mL.

Measuring Mass

  • During a physical examination, a doctor's office records mass in kilograms (kg), while lab results use grams (g), milligrams (mg), or micrograms (μg).

  • Equalities:

Learning Check 2

  • Task: Identify the larger unit among the following choices:

    • A: mm or cm

    • B: kg or cg

    • C: mL or µL

    • D: kL or mL

Solution 2

  • Answer Key:

    • A: A millimeter (mm) = 0.001 m, smaller than a centimeter (cm) = 0.01 m.

    • B: A kilogram (kg) = 1000 g, larger than a centigram (cg) = 0.01 g.

    • C: A milliliter (mL) = 0.001 L, larger than a microliter (µL) = 0.000001 L.

    • D: A kiloliter (kL) = 1000 L, larger than a microliter (mcL) = 0.000001 L.

Appendix 1

  • Description: Comparing measurements of a cube and a syringe.

    • A cube with dimensions 10 cm × 10 cm × 10 cm consists of smaller cubes 1 cm × 1 cm × 1 cm.

    • A 5 mL syringe can hold 1 mL of liquid, indicating that:

    • Volume of the cube = 10extcmimes10extcmimes10extcm=1000extcm3=1000extmL=1extL10 ext{ cm} imes 10 ext{ cm} imes 10 ext{ cm} = 1000 ext{ cm}^3 = 1000 ext{ mL} = 1 ext{ L}.

    • Volume of 1 cm³ cube = 1 mL.

    • Each segment of the 5 mL syringe is further divided into 5 equal parts, measuring liquid to the 1 mL mark.

  • Equivalences: 1.0extmL=1.0extcm3=1.0extcc1.0 ext{ mL} = 1.0 ext{ cm}^3 = 1.0 ext{ cc}.