Scientific Method and Unit Conversions

Scientific Method

While the scientific method can be defined in several different ways, the following sequence outlines the more important points:

  1. Question - Defines the problem to be studied.
  2. Hypothesis - An untested explanation.
  3. Experiment - Designed to test the hypothesis.
  4. Observation - Examine results of the experiment.

Steps 2-4 of this sequence are then repeated, refining the hypothesis at each stage as necessary to explain all experimental observations. As the amount of testing increases, a hypothesis can turn into a Theory, which can eventually become a scientific Law.

Significant Digits

In general, the accuracy of any mathematical operation is limited by the least precise value. This precision is commonly estimated using significant digits. The following rules can be used to estimate the number of significant digits in any value.

  1. The digits 1-9 are always significant.
  2. Any zero (0) between two non-zero digits are always significant.
  3. For numbers less than 0.1, none of the leading zeros are significant. Any trailing zeros are significant
  4. For numbers greater than 9, zeroes to the right of the last non-zero digit (1-9) may or may not be significant. We will assume that these zeros are not significant. (See your textbook for the proper treatment of these zeros).

For multiplication and division, the number of significant digits in the answer is equal to the number of significant digits in the value with the fewest number of significant digits.

3.005 x 1.48 = 4.4474 or 4.45
4 sig. digits 3 sig. digits Limited to 3 sig. digits

Scientific Notation

Scientific Notation is a convenient method for representing very large and very small numbers. In scientific notation, a number between 1 and 10 is multipled by ten raised to a power (the exponent). The exponent indicates the number of places to shift the decimal point. Positive exponents indicate large numbers, while negative exponents indicate small values.

6.54 x 10+3 = 6.54 x 1000 = 6540
1.23 x 10-4 = 1.23 x 0.0001 = 0.000123

Metric System

Scientists typically report data using the metric system. This system has the advantages of being based on powers of ten, and being accepted worldwide.

Base Units Approximate English Equivalent Related
meter yard 1 mile ≈ 1.6 km
liter quart 1 fl. oz ≈ 30 mL
gram 1/28 oz 1 kilogram ≈ 2 pounds
Metric Prefix Abbrev. Factor
kilo- k 1000
deci- d 0.1
centi- c 0.01
milli- m 0.001
micro- µ 10-6

Unit Conversions

See your textbook and the handout available on the course web site for more information on these types of problems.

Density

Density is defined as (mass)/(volume). This is a property of matter that does not depend on the amount of material present. Given any two of these three variables, you should be able to solve for the missing third value.

Equation Note
d = m / V (Given)
m = d * V To solve for mass
V = m / d To solve for volume

Heat

Heat is a property of matter that does depend on the amount. Typical problems are designed to determine the amount of heat required to heat (or cool) an object from an initial temperature to its final temperature. The equation we will use is:

q = m * S * ΔT

q = heat (in calories) m = mass of material (usually in grams) S = specific heat (in cal / (g * Co) ΔT = change in temperature