# Appendix D | Units and Conversion Factors

 Factor Name Abbreviation Factor Name Abbreviation 101 deca da 10-1 deci d 102 hecto h 10-2 centi c 103 kilo k 10-3 milli m 106 mega M 10-6 micro µ 109 giga G 10-9 nano n 1012 tera T 10-12 pico p 1015 peta P 10-15 femto f 1018 exa E 10-18 atto a 1021 zetta Z 10-21 zepto z 1024 yotta Y 10-24 yocto y

Table D.1 SI prefixes

 SI unit: metre (m) 1 metre (m) ≈ 39.37 inches (in.) 1 centimetre (cm) = 0.01 m 1 millimetre (mm) = 0.001 m 1 kilometre (km) = 1000 m 1 angstrom (Å) = 10-8 cm = 10-10 m 1 inch (in.) = 2.54 cm (exact, definition)

Table D.2 Units of Length

 SI unit: cubic metre (m3) 1 litre (L) = 0.001 m3 = 1000 cm3 1 millilitre (mL) = 0.001 L = 1 cm3 1 microlitre (µL) = 10-6 L = 10-3 cm3

Table D.3 Units of Volume

 SI unit: kilogram (kg) 1 gram (g) = 0.001 kg 1 milligram (mg) = 0.001 g 1 kilogram (kg) = 1000 g ≈ 2.205 lb 1 ton (metric) = 1000 kg 1 pound (lb) ≈ 0.4535924 kg = 16 ounces 1 atomic mass unit (amu) ≈ 1.66054 × 10-27 kg

Table D.4 Units of Mass

 SI unit: joule (J) 1 joule (J) = 1 kg • m2/s2 ≈ 9.4778 × 10-4 BTU1 1 thermochemical calorie (cal) ≈ 4.184 J ≈ 4.184 × 107  erg 1 erg = 10-7 J 1 electron-volt (eV) ≈ 1.60218 × 10-19 J ≈ 23.061 kcal mol−1 1 nutritional calorie (Cal) = 1000 cal ≈ 4184 J

Table D.5 Units of Energy

 SI unit: kelvin (K) 0 kelvin (K) = -273.15°C = -459.67°F K = °C + 273.15 °C = 59 (°F – 32) °F = 95 (°C) + 32

Table D.6 Units of Temperature

 SI unit: pascal (Pa) 1 pascal (Pa) = N m-2 = kg m-1 s-2 1 Torr = 1 mm Hg 1 atmosphere (atm) = 760 mm Hg = 760 Torr = 101 325 N m-2 = 101 325 Pa = 1.01325 bar 1 bar = 105 Pa = 105 kg m–1 s–2

Table D.7 Units of Pressure

Dimensional Analysis

Dimensional analysis is a form of proportional reasoning. It uses conversion factors to convert a quantity from one unit to another.

 Quantity with desired unit = Quantity with given unit × Conversion factor

In general, this method starts with the given value that will then be multiplied or divided by a known ratio or proportion. When setting up the ratios, the unit in the denominator must match that of the numerator of the given value. Continuing with the unit of the numerator in the next ratio, it has to match the denominator of the following ratio or of the units necessary for the answer.

3.41g×1mole4.002g×6.022×1023atoms1mole=5.13×1023atoms

Flipping the Conversion Factor

Note that a conversion factor can be flipped. For example, days are converted to hours by multiplying the days by the conversion factor of 24. The conversion can be reversed by dividing the hours by 24 to get days. The reciprocal 1/24 could be considered the reverse conversion factor for an hours-to-days conversion. The term “conversion factor” is the multiplier, not divisor, which yields the result.

Consider the following relationship

1kg1000g=1000g1kg

Both fractions are equal to 1 when the units are ignored. As the quotients are

both equal to 1, it does not change the equation, just the relative numerical values with

various units.

Solving Dimensional Analysis Problems

When doing dimensional analysis problems, follow this list of steps:

Identify the given amount with the given units (see previous concept for additional information).

Set up your equation so that your undesired units cancel out to give you your desired units. A unit will cancel out if it appears in both the numerator and the denominator during the equation.

Multiply through to get your final answer. Don’t forget the units and sig figs!

Example Problems

How many hours are in 3 days?

Solution:

1. Identify the given: 3 days

24hours1day

3. Set up your equation so that your undesired units cancel out to give you your desired units: 3 days ×

24hours1day

Converting between moles and grams

Find the amount of moles in 22.34 g of water.

Solution

22.34gH2O×1molH2O18gH2O=1.24molesH2O