Being Quantitative: Being Exact and Estimating
Being Exact
Units
this is very important: witness the Mars probe disaster and consider the many different unti systems used in designing the International Space Station
Significant digits
1.2 divided by 7 does not equal 0.17142857...
1.2 divided by 7 equals 0.2
0.2 also does not equal 0.20
Principle: The results can not be any more precise than the numbers that were inputted, ie. Garbage In, Garbage Out.
Specifying Accurately
- Physical Measurement (all measuring devices have a certain level of fidelity)
- Through Calculations
Example: Weather Predictions.
In the United States, four different numerical models are run five times a day. They are based on empircal data collected by weather stations that are based (on land) about 100 kilometers apart. Considering that the weather in New England changes if one drives just 30 kilometers, is it right for weathermen to claim to be able to predict the weather very accurately?
Identifying Clearly (Defining)
Be careful of all terms, particularly technical ones.
Estimating and Bounding
Estimation skills come from experience because one is then able to compare unknown quantities to known quantities
Bounding is knowing what the limits are
Example: If one sees liquid water, one can say that the temperature is greater than 32 degrees F and less than 212 degrees F.
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