Chemistry 11: S.I. Units and Standard Prefixes

• Accurate measurements are essential for good science, focusing on measurement and calculation skills

S.I. Units

• S.I. Units are used for most measurements in Chemistry 11

• Length is measured in Metres (m), with 'm' as the lowercase abbreviation

• Mass is measured in Kilograms (kg), representing the amount of matter in an object; weighing measures mass

• Time is measured in Seconds (s), with 's' as the lowercase abbreviation

• Temperature is measured in Kelvins (K), where zero Kelvins is absolute zero

• Temperature in Kelvins equals degrees Celsius (°C) plus 273

• On a warm day, a temperature of 28°C is equal to 301 K

Standard Prefixes

• Prefixes adjust S.I. units to be larger or smaller, applicable to any unit of measurement
• Giga (G) equals 1,000,000,000
  • 1 Gigametre (Gm) equals 1,000,000,000 metres
• Mega (M) equals 1,000,000
  • 1 Megagram (Mg) equals 1,000,000 grams
• Kilo (k) equals 1,000
  • 1 Kilometre (km) equals 1,000 metres
• deci (d) equals 1/10 or 0.1
  • 1 Decisecond (ds) equals 0.1 second
• centi (c) equals 1/100 or 0.01
  • 1 Centimetre (cm) equals 0.01 metre
• Milli (m) equals 1/1,000 or 0.001
  • 1 Milligram (mg) equals 0.001 gram
• Micro (μ) equals 1/1,000,000 or 0.000 001
  • 1 Micrometre (µm) equals 0.000 001 metre
• Nano (n) equals 1/1,000,000,000 or 0.000 000 001
  • 1 Nanosecond (ns) equals 0.000 000 001 second

Other Important Units

• These are not S.I. units but are commonly used by scientists
• 1 Litre (L) equals 1,000 cm³
  • 1,000 L equals 1 m³
  • cm³ stands for cubic centimetre, and m³ stands for cubic metre
• 1 Millilitre (mL) equals 1 cm³
  • 1,000 mL equals 1 L

Significant Figures

• It's important to be conservative in treating numbers, assuming the last significant figure is the last non-zero digit unless given more information

• Trailing zeroes are not significant figures; they are space fillers

• In 2,228,400, there are five significant figures: 2,228,4

• In 40,200 metres, there are three significant figures: 40,2, the length is precise to the 100's of metres

• In 40,200.00 metres, there are seven significant figures

• For large numbers with decimal points, every digit from the beginning to the decimal point is significant, along with any digits to the right of the decimal point

• 10,000.0 has 6 sig figs

• 890. has 3 sig figs

• 890 has 2 sig figs (no decimal point, so have a trailing zero)

• 78.0020 has 6 sig figs

• For numbers smaller than one (decimal fractions), leading zeroes are place keepers

• The first non-zero digit is the first significant figure

• 0.0087 has two sig. figs; the '8' and the '7'

• 0.0200 has three sig. figs; the '2', and the zeroes to its right

Scientific Notation

• Scientific notation uses powers of ten to handle very large or very small numbers

• Power of ten indicates how many tens are multiplied together within the number

• 100 = 10 x 10 = 10² (2 tens multiplied)

• 1,000 = 10 x 10 x 10 = 10³

• 10,000 = 10 x 10 x 10 x 10 = 10⁴

• 100,000 = 10 x 10 x 10 x 10 x 10 = 10⁵

• Smaller numbers than one have negative powers

• 0.1 = 1/10 = 10⁻¹

• 0.01 = 1/10 x 1/10 = 10⁻²

• 0.001 = 1/10 x 1/10 x 1/10 = 10⁻³

• A decimal fraction starting in the 2nd decimal place has a power of negative two; in the 3rd decimal place, a power of negative three

Converting to Scientific Notation

• Step one, determine the number of significant figures

• One digit should be to the left of the decimal place

• All other significant figures should be to the right of the decimal place

• 42,600 converts to 4.26 x 10⁴

• 42.6 x 10³ is incorrect

• Step two, determine the power of 10 by counting from the one's place to the digit at the front of the number

• The quantity should be moved 4 places to the left from 42600 to get the ‘0’ at ones place to the ‘4’ at the front of the number

• Decimal fractions can also be converted into scientific notation

• 0.082 converts to 8.2 x 10⁻²

Converting Decimal Fractions to Scientific Notation

• Step one, use the amount of significant figures in the number "8.2"

• Step two, for decimal fractions it is easy

• Find the power because the power is always equal to the decimal place were it begins

• 1.62 converts to 1.62 x 10⁰

Uncertainty and Significant Figures

• Precision relates to how fine a measurement is, indicated by the number of decimal places

  • 5.728 mm is precise to the 3rd decimal place, while 5.7 mm is precise to the 1st decimal place

• Accuracy relates to how close a measurement is to the true value

• A book is 31.2 cm long

• Student #1 measures 29.482 cm

• Student #2 measures 31.1 cm

• Student #2 is more accurate even though Student #1 is more precise

Standard Uncertainties

• Ruler: ± 1 mm (same as ± 0.1 cm), measured to the nearest whole mm
• Thermometer: ± 1 °C, measured to the nearest whole degree Ex: 17 °C - CORRECT, 17.5 °C - INCORRECT
• Centigram Balance: ± 0.01 gram, measured to the 2nd decimal place

Ex: 20.20 g - CORRECT, 20.2 g - INCORRECT

• Buret: ±0.1 mL, measured to the 1st decimal place

Determining Uncertainty

• Outside of the classroom the uncertainties can be different, because different equipment is being used
• Through repeatably taking measurements, one can determine the reliability of the equipment.
• A reading of his copper is measured to be 1.014 mm, but his measurement is with in 0.003 mm bigger or smaller with his micrometer: 1.014 ± 0.003 mm

Unit Conversions

• Multiplying the measurement by a conversion factor solves this problem

• The conversion factor includes what unit you want (on top), the unit you start with (on the bottom), and the conversion number that equates the two units

• 75,290 mm converted into metres equals 75.29 m

• 11.8 km² converted into units of m² equals 11,800,000 m²

  • So square all of the unites and numbers for the conversion factor to convert a km² to m² (1,000² = 1,000,000 & 1² = 1)

• 8,540,000 µm² converted into units of mm² using the formula

  • Conversion Number = Milli/micro
  • Since both are squared, the new conversion number is 1,000² = 1,000,000
• • 8,540,000 µm² = 8.54 mm²

• A car going at 25.4 km/h is equal to 7.06 m/s after converting it, there for both figures have 3 significant figures

  • Put km on the bottom to cancel out the km of km/h
  • Put h on top to cancel out the 'per h' of km/