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Learn why all science experiments have error, how to calculate it, and the sources and types of errors you should report.

SI prefixes Factor Name Symbol 10 24 yotta Y 10 21 zetta Z 10 18 exa E 10 15 peta P 10 12 tera T 10 9 giga G 10 6 mega M 10 3 kilo k 10 2 hecto h 10 1 deka da Factor Name Symbol 10 -1 deci d 10 -2 centi c 10 -3 milli m 10 -6 micro µ 10 -9 nano n 10 -12 pico p 10 -15 femto f 10 -18 atto a 10 -21 zepto z 10 -24 yocto y Fundamental and Derived Quantities Physical quantities are not generally independent of one another. Many quantities can be expressed in terms of more fundamental quantities. The first three fundamental quantities we will deal with are those of mass, length and time. Many derived quantities can be expressed in terms of these three. For example, the derived quantity speed can be expressed as length/time.

Note that there are seven fundamental quantities in all. The other four are: current, thermodynamic temperature, amount of substance and luminous intensity. We will deal with these as we need them.

Dimensions The expression of a derived quantity in terms of fundamental quantities is called the dimension of the derived quantity. The symbol M is used to denote the dimension of mass, as is L for length and T for time. So, for example, to determine the dimensions of the derived quantity speed, we would look at the formula for speed, namely: speed = distance/time The dimensions of speed are then: [speed] = [distance] / [time] = L / T where the square brackets are used to indicate that we are calculating the dimensions of whatever is inside the brackets. Finally, we use our knowledge of indices to simplify this expression. [speed] = LT -1 Question: Determine the dimensions of (a) area and (b) volume. Answers: (a) L 2; (b) L 3. Dimensions can be used to check the correctness of an equation.

The dimensions of the left hand side of the equation must equal the dimensions of the right hand side. Dimensions can also be used to verify that different mathematical expressions for a given quantity are equivalent.

Question: Given the formulas for the following derived quantities, calculate the dimensions of each quantity. Velocity = displacement/time b. Acceleration = change of velocity/time c. Momentum = mass x velocity d.

Force = mass x acceleration e. Work = force x displacement Answers: a. Significant Figures Since the precision of all measuring instruments is limited, the number of digits that can be assumed as known for any measurement is also limited. When making a measurement, read the instrument to its smallest scale division. Estimate within a part of a division. The figures you write down for the measurement are called significant figures.

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