The SI System

Measurements and Calculations

Système Internationale d'Unités (SI)

• an internationally agreed upon system of measurements.

• Decimal system (all conversions based on multiples of 10) • SI consists of seven base units.

Base Unit: defined unit in a system of measurement that is based on an object or event in the physical world, and is independent of other units.

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1 mL = 1 cm 3

1 milliliter is the same volume as 1 cubic centimeter.

1 mL of water has a mass of approximately 1 g

The mass of 1 milliliter of water is approximately 1 gram.

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1 L of water has a mass of approximately 1 kg

The mass of 1 liter of water is therefore approximately 1 kilogram.

1 m 3 of water has a mass of approximately 1 t

There are 1000 liters in a cubic meter, so the mass of 1 cubic meter of water is approximately 1000 kilograms or 1 metric ton.

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Mass of a nickel is 5 g

A US nickel weighs 5 grams, and a penny weighs 2.5 grams.

A typical doorknob is 1 m high

Although there's no precise standard for doorknob heights, they're often about 1 meter above the floor.

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The diameter of a CD or DVD is 12 cm

A CD or DVD is 12 centimeters (120 millimeters) across. The diameter of the center hole is 15 millimeters.

1 ha is 100 2 m 2

1 hectare is 10 000 square meters, equivalent to the area of a square 100 meters on a side. A football field is about 100 meters long, so imagine a square the length of a football field on each side, and that's 1 hectare.

Base Units

 The SI base unit of time is the second (s), based on the frequency of radiation given off by a cesium-133 atom.

 The SI base unit for length is the meter (m), the distance light travels in a vacuum in 1/299,792,458th of a second.  The SI base unit of mass is the kilogram pounds (kg), about 2.2

SI Base Units

MANY DERIVED UNITS

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Quantity Unit Abbreviation

Speed = Length/Time meter/second Volume =(Length) 3 (meter) 3 Density = Mass/Volume kg/m 3 Acceleration = speed/time Force = Mass x Acc m/s 2 kg m/ s 2 Pressure = Force/Area kg/m s 2 Energy = Force x Length kg m 2 / s 2 J (Joule) m/s m 3 kg/m 3 m/s N (Newton) Pa (Pascal) 2

Prefix Symbol yotta zetta exa peta tera giga mega kilo hecto deca no prefix (base unit) Y Z E P T G M k h da deci centi milli micro nano pico femto atto zepto yocto n p f a z y d c m

m

Exponential 10 24 10 21 10 18 10 15 10 12 10 9 10 6 10 3 10 2 10 1 10 0 10¯ 1 10¯ 2 10¯ 3 10¯ 6 10¯ 9 10¯ 12 10¯ 15 10¯ 18 10¯ 21 10¯ 24

Converting between SI Units

     Use the chart like this: 1 prefixed unit = exponential value of the prefix 1 cm = 10 -2 m 1 nm = 10 -9 m 1 Mm = 10 6 m Example:

Measurements of Length

 Base Unit: the Meter      Centimeter Millimeter Nanometer Micrometer Picometer

Measurement of Mass

 Base Unit: the kilogram (the gram is too small) only prefixed base unit

Measurement of Time

 Base Unit: the second

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Measurement of Temperature

A measure of how hot or how cold something is A quantity that determines the direction of heat flow: warmer to cooler Three temperature scales commonly used:  Celsius   Kelvin (absolute) Fahrenheit

To Convert F to C

   1.8 degrees F = 1 degree C F = 32 + (1.8 x degrees C) Example: Convert 22 degrees C to degrees F   C = F – 32/1.8

Example: Convert 98.6 degrees F to degrees C.

To Convert Celsius to Kelvin

  0 degrees C = 273 K K = C + 273  C = K -273

Examples:

Convert 100 degrees C to Kelvin.

Convert 475 K to degrees C Convert 250 K to degrees C.

Derived Units

Volume and Density Calculations

Volume

       Base Unit : m 3 Not practical because it is very large Commonly used: dm 3 Also called “THE LITER (L)” 1 dm = 10 cm 1 cm 3 = 1mL 1 dm 3 = 1 L NOTE: 1 dm 3 = (10 cm) 3 = 1000 mL= 1000 cm 3 = 1L Example: Calculate the volume of a cube that is 3.30 cm on each side.

Density

    Mass to volume ratio The mass of a unit volume density = mass/volume d = m/v

Examples

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Calculate the density of a piece of glass with a mass of 6.65 g and a volume of 2.95 mL.

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Calculate the thickness of an aluminum foil 15.38 cm long and 14.39 cm wide. The mass of the foil is 1.4939 g. The density of aluminum is 2.70 g/cm 3 . (HINT: We consider the Aluminum foil to be a rectangular solid).

Dimensional Analysis (Factor Label)

    Method of calculating using the units Makes word problems and chemistry calculations easy!

Any unit can be converted to another by using appropriate conversion factors Start unit x final unit = final unit start unit Conversion factors (equalities written as fractions)

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Example

On a picnic, 162 students are each given 2 hot dogs. If there are 9 hot dogs per pound, priced at $ 4 per 3 pounds, what is the cost of the hot dogs?

     Note that the following conversion factors can be obtained from the text of the problem: 1 student = 2 hotdogs 9 hot dogs = 1 lb $4 = 3 lbs To begin solving the problem, start with a known and keep your goal in mind:  Note that all the units (except $) cancel out!