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**Measurements and Calculations**

The SI System Measurements and Calculations

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**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 milliliter is the same volume as 1 cubic centimeter.**

1 mL = 1 cm3 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. 1 L of water has a mass of approximately 1 kg The mass of 1 liter of water is therefore approximately 1 kilogram. 1 m3 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 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 1002 m2 1 hectare is 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.

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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 (kg), about 2.2 pounds

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SI Base Units

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**MANY DERIVED UNITS Quantity Unit Abbreviation**

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

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Prefix Symbol Exponential yotta Y 1024 zetta Z 1021 exa E 1018 peta P 1015 tera T 1012 giga G 109 mega M 106 kilo k 103 hecto h 102 deca da 101 no prefix (base unit) 100 deci d 10¯1 centi c 10¯2 milli m 10¯3 micro 10¯6 nano n 10¯9 pico p 10¯12 femto f 10¯15 atto a 10¯18 zepto z 10¯21 yocto y 10¯24

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**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 = 106 m Example:

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**Measurements of Length**

Base Unit: the Meter Centimeter Millimeter Nanometer Micrometer Picometer

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**Measurement of Mass Measurement of Time**

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

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**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.

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**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 K to degrees C.

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**Volume and Density Calculations**

Derived Units Volume and Density Calculations

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**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.

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**Density Mass to volume ratio The mass of a unit volume**

density = mass/volume d = m/v

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Examples Calculate the density of a piece of glass with a mass of g and a volume of 2.95 mL. Calculate the thickness of an aluminum foil cm long and cm wide. The mass of the foil is g. The density of aluminum is 2.70 g/cm 3 . (HINT: We consider the Aluminum foil to be a rectangular solid).

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**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!

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Measurements in Physics

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