Measuring and Calculating

1. Measuring and Calculating Chapter 3A

2. What is Measuring? • Measurement • Is the act of comparing an unknown quantity to a standard unit. • Objects and systems are measurable. • What are some examples of measurements? • Length • Mass • Volume • Time • Electrical charge • Temperature • Velocity • Each of these properties is called a dimension. • Before a dimension can be measured, it must have a unit of measure defined for that dimension.

3. Unit of Measurement • The word “Unit” means 1 of something • What are some examples of common units? • Meter, Inches, Liters, Gallons • So how is a unit determined? • Dimensional units are lined up on a scale to provide a means of measuring. • A scale is calibrated, or accurately divided into measurement units. • An instrument is any artificial device made for the purpose of refining, extending, or substituting for the human senses when measuring. • A measurement consists of 2 parts • The number • The unit in which the measurement was taken • If either is missing the answer is wrong • Only like units can be added or subtracted • Any unit can be multiplied or divided

4. Metric System of Measurement • In the 18th century the need or standardized units spurred the development of the metric system. • The metric system is based on a decimal scale • A scale that consists of base units multiplied or subdivided by powers of 10 • France became the 1st country to adopt the metric system consisting of the kilogram and the meter. • They manufactured a standard out of platinum metal in the form of a cylinder and bar respectively. • In the 196.’s many counties adopted the metric system called the International System of Units (Système, International d’Unités) commonly abbreviated to SI units.

5. SI Units • Base SI Units • There are 7 base units in the SI, each measuring a basic dimension.

6. SI Units • Nearly every other unit of measure can be expressed in terms of these base units • This sometimes these are hard to remember or take too much time when writing them down • So special units called derived units were established. • There are 22 derived units approved for used in the SI • Example 1J=1kg*m2/s2

7. Commonly Derived Units

8. Selected Non-SI Units

9. SI Unit Prefixes • With SI units you can express quantities in different sizes • To change the size of a unit you add a prefix that represents a power of ten to the base unit. • For example a meter is the base SI unit, but that is not always a convenient size to use • So 1/100 of a meter is a centimeter

10. SI Unit Prefixes

11. Conversion • Values can be converted by multiplying by the appropriate factor of 10 • So you are just moving the decimal point left or right • Often times you will have items of the same dimension but have different SI units so you will need to do a unit conversion • Unit conversions involve multiplying a measurement by a conversion factor. • A conversion factor is a fraction that contains both the original unit and its equivalent value in a new unit. • Mathematically the fraction is equal to 1

12. Bridge Notation • Bridge notation is a special notation for multiplying and dividing several units at the same time. • The notation has its name because it looks like a trestle bridge • Bridge notation can be used for any calculation but is almost always used when converting units. • Bridge notation only applies to multiplication and division and cannot be used for addition and subtraction • It requires that each measurement be written as a fraction with a numerator and denominator. • Measurements and units that are not naturally ratios are written as a fraction with 1 in the denominator

13. Conversions • Convert the following using the bridge notation: 132,540cm to kilometers 132 540 cm 132 540 1 m 1 km 1.32540 km = = 100 000 100 cm 1000 m 1

14. Conversions • Convert the following using the bridge notation: 350 mg to kilometers How would you write that in exponential notation? 3.50 X 10-4 kg 350 mg 350 1 g 1 kg 0.000350 gm = = 1 000 000 1000 mg 1000 g 1