Fundamental Units: units that are defined by a basic unit of measurement. These are units that are based on a specific definition and given a constant fixed value upon which to base a single unit of the measurement. time: Seconds (s or sec) This is the basic unit that all time measurements are made in. Since 1967, the basis for the second is 9,192,631,770 cycles of the radiation of a cesium atom in its lowest two energy states. distance: meters (m) This is the basic unit for all other measurements of length, position, or separation between objects or points. Since 1983, the meter is defined as the distance light will travel in a vacuum in 1/299,792,458th of a second. (The speed of light in a vacuum is exactly 299,792,458 meters per second!) mass: kilogram (kg) This is the basic unit for all measurements for how much matter there is in an object. Currently it is based on the mass of a particular cylindrical quantity of a platinum-iridium alloy currently kept at the Bureau of Weights and Measures at Sevres in France. Derived Units: Units that are determined by a formula using the fundamental units. They are determined because a calculation was made with the fundamental units. e.g. Speed - distance traveled in a certain amount of time. Calculated by dividing distance by time. Units for speed are meters per second (m/s). Scientific Notation: A short hand method for writing very large or very small numbers. e.g. The speed of light for all intents and purposes is 300,000,000 m/s. [See above for the exact value.] In scientific 8 notation this can be written as 3.00×10 m/s. 23 Avogadro’s Number is 602,213,673,600,000,000,000,000. In scientific notation this is 6.022×10 atoms (molecules) per mole. The thickness of a sheet of paper is approximately 0.0002 meters. In scientific notation this can be written -4 as 2.0×10 meters. When you add or subtract numbers that are in scientific notation, their powers of ten must be the same. ex. 4.5 × 105 + 6.1× 103 = 4.5 × 105 + 0.061×105 = 4.561× 105 When you multiply numbers that are in scientific notation, you simply multiply the numbers and add the powers of ten. ex. 2.0 × 10-3 × 4.0 × 10 2 = (2.0 × 4.0) ×10(-3+2) = 8.0 × 10-1 When you divide, simply divide the numbers and subtract the powers of ten. - 1.4 ( 4−2 ) ex. - 1.4 × 10 4 ÷ 7.0 × 10 2 = ×10 = −0.2 × 10 2 = −2.0 × 101 7.0 Uncertainty of Measurement Error happens anytime you try to measure something. This is because the devices we use to make a measurement are not perfectly precise. Sometimes, simply the way we look at the measuring device can create error. Parallax: the apparent shift of the needle or measurement mark of a measuring device when not viewed from directly above the needle or mark. Parallax can be caused simply by looking at a measuring device without closing one of your eyes. There are two basic kinds of error: Absolute and Percent. Absolute Error comes from imprecision in the measuring device. This depends on how small the divisions are on the measuring device. This error is indicated by using a “±” with the smallest division on the measuring device. ex. A ruler can measure to the nearest millimeter. The width of a block may have a measurement of 4.0 cm ± 0.1 cm (0.1 cm = 1 mm) Percent Error shows the difference between an expected value for a measurement, and the calculated value determined from your measurements. To determine percent error, use the following formula: Theoretical - Observed Percent Error = × 100% Theoretical Theoretical means the expected value you were aiming for with your measurement. Observed means the value of the measurement you calculated or measured. Notice: the |Absolute Value| symbol in the numerator. There are no negative percent errors!
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