Chemistry and Measurements: Prefixes and Equalities

Prefixes and Equalities

  • Learning Goal: Use the numerical values of metric prefixes to write an equality.

Prefixes

  • In the metric and SI systems, a prefix modifies a unit's size by a factor of 10.
  • 1 kilometer (1 km)=1000 m1 \text{ kilometer (1 km)} = 1000 \text{ m}
  • 1 millimeter (1 mm)=0.001 m1 \text{ millimeter (1 mm)} = 0.001 \text{ m}

Prefixes and Equalities

  • The relationship between a prefix and a unit is expressed by replacing the prefix with its numerical value.
  • Example:
    • 1 kilometer=1000 meters1 \text{ kilometer} = 1000 \text{ meters}
    • 1 kiloliter=1000 liters1 \text{ kiloliter} = 1000 \text{ liters}
    • 1 kilogram=1000 grams1 \text{ kilogram} = 1000 \text{ grams}

Metric and SI Prefixes That Increase the Size of the Unit

PrefixSymbolNumerical ValueScientific NotationEquality
petaP1,000,000,000,000,000101510^{15}1 Pg=1×1015 g1 \text{ Pg} = 1 \times 10^{15} \text{ g}, 1 g=1×10−15 Pg1 \text{ g} = 1 \times 10^{-15} \text{ Pg}
teraT1,000,000,000,000101210^{12}1 Ts=1×1012 s1 \text{ Ts} = 1 \times 10^{12} \text{ s}, 1 s=1×10−12 Ts1 \text{ s} = 1 \times 10^{-12} \text{ Ts}
gigaG1,000,000,00010910^91 Gm=1×109 m1 \text{ Gm} = 1 \times 10^9 \text{ m}, 1 m=1×10−9 Gm1 \text{ m} = 1 \times 10^{-9} \text{ Gm}
megaM1,000,00010610^61 Mg=1×106 g1 \text{ Mg} = 1 \times 10^6 \text{ g}, 1 g=1×10−6 Mg1 \text{ g} = 1 \times 10^{-6} \text{ Mg}
kilok1,00010310^31 km=1×103 m1 \text{ km} = 1 \times 10^3 \text{ m}, 1 m=1×10−3 km1 \text{ m} = 1 \times 10^{-3} \text{ km}

Metric and SI Prefixes That Decrease the Size of the Unit

PrefixSymbolNumerical ValueScientific NotationEquality
decid0.110−110^{-1}1 dL=1×10−1 L1 \text{ dL} = 1 \times 10^{-1} \text{ L}, 1 L=1×101 dL1 \text{ L} = 1 \times 10^{1} \text{ dL}
centic0.0110−210^{-2}1 cm=1×10−2 m1 \text{ cm} = 1 \times 10^{-2} \text{ m}, 1 m=100 cm1 \text{ m} = 100 \text{ cm}
millim0.00110−310^{-3}1 ms=1×10−3 s1 \text{ ms} = 1 \times 10^{-3} \text{ s}, 1 s=1×103 ms1 \text{ s} = 1 \times 10^{3} \text{ ms}
microμ\mu0.000 00110−610^{-6}1μg=1×10−6 g1 \mu \text{g} = 1 \times 10^{-6} \text{ g}, 1 g=1×106μg1 \text{ g} = 1 \times 10^{6} \mu \text{g}
nanon0.000 000 00110−910^{-9}1 nm=1×10−9 m1 \text{ nm} = 1 \times 10^{-9} \text{ m}, 1 m=1×109 nm1 \text{ m} = 1 \times 10^{9} \text{ nm}
picop0.000 000 000 00110−1210^{-12}1 ps=1×10−12 s1 \text{ ps} = 1 \times 10^{-12} \text{ s}, 1 s=1×1012 ps1 \text{ s} = 1 \times 10^{12} \text{ ps}
femtof0.000 000 000 000 00110−1510^{-15}1 fs=1×10−15 s1 \text{ fs} = 1 \times 10^{-15} \text{ s}, 1 s=1×1015 fs1 \text{ s} = 1 \times 10^{15} \text{ fs}
  • In medicine, 'mc' is used for micro to avoid misreading μ\mu. For example: 1 mcg.

Daily Values for Selected Nutrients

The U.S. Food and Drug Administration uses metric prefixes to express amounts of daily nutrient requirements.

NutrientAmount Recommended
Calcium1.0 g1.0 \text{ g}
Copper2 mg2 \text{ mg}
Iodine150μg150 \mu \text{g}
Iron18 mg18 \text{ mg}
Magnesium400 mg400 \text{ mg}
Niacin20 mg20 \text{ mg}
Phosphorus800 mg800 \text{ mg}
Potassium3.5 g3.5 \text{ g}
Selenium70μg70 \mu \text{g}
Sodium2.4 g2.4 \text{ g}
Zinc15 mg15 \text{ mg}

Measuring Length

  • An equality shows the relationship between two units that measure the same quantity.
  • Metric length of 1 m is the same length as 10 dm, 100 cm, and 1000 mm.

Measuring Volume

  • Volumes of 1 L or smaller are common in the health sciences.
  • When a liter is divided into 10 equal portions, each portion is called a deciliter (dL).
  • The cubic centimeter (cc) is the volume of a cube with the dimensions of 1 cm×1 cm×1 cm1 \text{ cm} \times 1 \text{ cm} \times 1 \text{ cm}.
  • A cube measuring 10 cm on each side has a volume of 1000 cm31000 \text{ cm}^3, or 1 L.
  • A cube measuring 1 cm on each side has a volume of 1 cc, or 1 mL.
  • A cubic centimeter (cc) has the same volume as a milliliter (mL), and the units are often used interchangeably.

Measuring Mass

  • Mass is commonly recorded in kilograms (kg) and laboratory results in micrograms (μ\mug or mcg).