advertisement

Section 4 Base Units, Derived Units, and the Metric System Physical science involves extensive work with “quantitative values”.....numbers that are measurements or calculation results. All such numbers are communicated with units placed behind them...such as metres or hours, etc. There are two types of units : 1. Base Units : (FUNDAMENTAL, or DEFINED units) Any other calculation result or measurement may be written as a combination of these basic units. Length (distance) - meter (m) Time- second (s) Mass - kilogram (kg) Electric Current - ampere (A) Temperature - kelvin (K) Amount of substance - mole (mol) Luminous intensity - candela (cd) 2. Calculated (derived) values: Units that we “figure out” by using the base units in some type of calculation. Examples : Speed - m/s Acceleration - m/s2 Area - m2 Force - kg m/s2 (N) The Metric System ( SI system ) Since the 1960s the International System of Units ("Système International d'Unités" in French, hence "SI") has been the internationally recognised standard metric system. Metric units are widely used around the world for personal, commercial and scientific purposes. A standard set of prefixes in powers of ten may be used to derive larger and smaller units from the base units. The global use of a metric system is intended to provide a common standard for comparing or communicating science knowledge. Other system are in use ( like the older “imperial System of Measurement” still in use in the USA) The newer SI system uses powers of ten, nice and easy to use when doing conversions, rather than the Imperials odd conversions like 3 feet per yard, or 5760 feet in a mile. These are less friendly numbers to work with. A metric conversion is changing from any one unit to another, but for the purposes of this 1206 course, you are responsible for conversions to and from the “BASE UNIT” when you start anywhere between Giga and nano. Moving to the SI Unit Ex..... Convert 0.28 Megabytes to the SI unit (bytes). You must recognize that “mega” is the prefix, and “byte” is the SI unit being referred to. 1. 2. M is mega, or 106 Replace M with × 10 6 ... meaning we have 0.28 x 106 b OR... simply move the decimal point 6 places right 3. Convert this answer to scientific notation OR normal notation, your choice. Ex. 2.8 x 105 b Ex.... OR 280 000 b thing) (same Convert 4.3 µm to the SI unit. You’re supposed to recognize that µ is micro, meaning 10 -6 AND.... metres is the SI unit referred to. 1. 2. Replace µ with × 10 -6 , or simply move the decimal 6 places left Gives 4.3 × 10 -6 m or 0.000 004 3 m Moving From the SI Unit to something larger or smaller Ex. Convert 567 500 m into kilometres. 1. You should recognize that m is the base (SI) unit 2. You should recognize that “kilo” is × 10 3 , or simply move your decimal three places left. 3. 567 500 m, when the decimal moves three places, becomes 567.5 km (note the zeros are dropped because they were NOT significant digits in the number you started with) Remember : When you move from larger units ( the top ) downwards, numbers get bigger while the decimal point moves right. The opposite is true when moving upwards. Table 5. SI prefixes 1. . Factor Name Symbol 1024 1021 1018 1015 1012 109 106 103 102 101 yotta zetta exa peta tera giga mega kilo hecto deca Y Z E P T G M k h da ANY SI UNIT that doesn’t have a prefix Factor Name Symbol 10-1 10-2 10-3 10-6 10-9 deci centi milli micro nano d c m µ n 10-12 10-15 10-18 10-21 10-24 pico femto atto zepto yocto p f a z y When you are converting from a larger prefix to a smaller one, you multiply the number × 10 ?, and the exponent is always positive. In other words, move the decimal point “?” places to the right. The opposite is true when moving from a small prefix to a large one...the exponent is negative, so move the decimal to the left. One more conversion you’ll need... Examples time conversions # Days × 24 hrs / day = hours # Hours × 60 mins / hr = minutes # Minutes × 60 s / min = seconds Convert the following.... 0.45 kA to A 367 mg to g 4.6 x 10 3 μm to m