Scientific Notation is used to efficiently write extremely large and extremely small numbers. To convert a number to scientific notation, first move the decimal so that it is behind the first non-zero digit of the number:
0.0000783 becomes 7.83
109200000 becomes 1.092
109200000 becomes 1.092
Next, count how many places the decimal was moved. Multiply the number by 10 to the power of the number of places moved if the unconverted number was greater than one. If the unconverted number was less than one, multiply by 10 to the power of negative the number of places moved:
0.0000783 –> move the decimal five spaces –> 7.83
Less than one –> 7.83 * 10^-5
109200000 –> move the decimal eight spaces –> 1.092
Greater then one –> 1.092 * 10^8
Less than one –> 7.83 * 10^-5
109200000 –> move the decimal eight spaces –> 1.092
Greater then one –> 1.092 * 10^8
Optionally, enter this expression into a calculator to confirm that it is equal to the original unconverted number. To convert a number from scientific to standard notation, simply reverse the steps: move the decimal place on by the power to which 10 is raised, moving it to the left if the power is negative and to the right if the number is positive. Calculators may substitute the 10 in scientific notation for 'E':
7.83 * 10^-5 –> 7.83 E-5
However, 'e' represents a mathematical constant, and the letter should not be included in any handwritten scientific notation.
To convert between units, multiply the number with units by the ratio between the original units and the desired units, making sure that the original units appear on different sides of the fraction so they cancel:
To convert between units, multiply the number with units by the ratio between the original units and the desired units, making sure that the original units appear on different sides of the fraction so they cancel:
5 inches * (2.54cm/1in) = 12.7cm
Inches/Inches = 1
Inches/Inches = 1
Sometimes multiple conversions are needed of there is not a known relationship between two particular units. To get from unit A to unit C, multiply by the ratio of Unit B/Unit A, then by unit B/Unit C:
5 inches * (2.54cm/1in) * (10mm/1cm) = 127mm
Note that the units still cancel:
Inches/Inches = 1
Centimeters/Centimeters = 1
Note that the units still cancel:
Inches/Inches = 1
Centimeters/Centimeters = 1
For units which are rates, convert the numerator and the denominator separately, making sure that unwanted units cancel:
(100 miles/hour) * (1609m/1 mile) * (1 hour/60min) = 160900 meters/60 minutes = 2681 meters/minute
Miles/Miles = 1
Hours/Hours = 1
Miles/Miles = 1
Hours/Hours = 1
Linear models have a constant rate of change, their slope. The slope determines how much the dependent variable changes with the independent variable. For example, a slope of 3 meters/second means that for every second of change in time results in a 3 meter change in distance. With a linear model, this rate will be the same no matter how many meters or seconds. The equation for a linear model is Dependent variable = Slope * (DP units/IV units) * Independent variable + Dependent variable. Inverse and quadratic models do not have a constant slope, as it either increases or decreases as the independent variable increases. An inverse function's slope decreases, while a quadratic function's slope increases:
The Y or dependent variable intercept is the value of the dependent variable when the independent variable is zero. To minimize the effect of uncertainty, it is paramount that a large number of data points be tested with different values. At one extreme, if only two data points are collected, any kind of line or curve or straight line could pass through the points. While three points will reveal what kind of curve the model exhibits, 5 data points at minimum are recommended to be able to guess a fit. When finding a best fit line, the simplest mode is often the most accurate. To ensure a proper range of values is tested in an experiment, The largest tested independent variable value should be at least 10 times larger than the smallest. For example, when testing how mass of an object affects a dependent variable, the object should be tested with weights from 50 to 500 grams. To compensate for any inherent uncertainty in each measurement, at least three trials should be conducted for each independent variable value when applicable. For example, the timing of a period of a pendulum may change slightly across trials while the mass of an object will not.